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的问题,本文提出一种低复杂度最长链共识算法(Low-Complexity Longest-Chain Consensus, LCLCS)。其核心思想是引入网络动力学理论对最长链的传播与收敛过程进行连续时间建模,并在此基础上重构最长链选择策略的比较对象与触发时机:将节点的比较范围由全网竞争链收缩为稀疏拓扑中的直接邻居,将决策的触发方式由事件驱动改为周期性主动查询,辅以基于链权重的快速收敛机制,从而在保持最长链规则基本安全性的前提下,将通信复杂度由 ",[1099,1216,1218,1241],{"className":1217},[1102],[1099,1219,1221],{"className":1220},[1106],[1108,1222,1223],{"xmlns":1110},[1112,1224,1225,1239],{},[1115,1226,1227,1229,1231,1237],{},[1118,1228,1120],{},[1122,1230,1125],{"stretchy":1124},[1127,1232,1233,1235],{},[1118,1234,1131],{},[1133,1236,1135],{},[1122,1238,1138],{"stretchy":1124},[1140,1240,1143],{"encoding":1142},[1099,1242,1244],{"className":1243,"ariaHidden":1148},[1147],[1099,1245,1247,1250,1253,1256,1285],{"className":1246},[1152],[1099,1248],{"className":1249,"style":1157},[1156],[1099,1251,1120],{"className":1252,"style":1163},[1161,1162],[1099,1254,1125],{"className":1255},[1167],[1099,1257,1259,1262],{"className":1258},[1161],[1099,1260,1131],{"className":1261,"style":1174},[1161,1162],[1099,1263,1265],{"className":1264},[1178],[1099,1266,1268],{"className":1267},[1182],[1099,1269,1271],{"className":1270},[1186],[1099,1272,1274],{"className":1273,"style":1191},[1190],[1099,1275,1276,1279],{"style":1194},[1099,1277],{"className":1278,"style":1199},[1198],[1099,1280,1282],{"className":1281},[1203,1204,1205,1206],[1099,1283,1135],{"className":1284},[1161,1206],[1099,1286,1138],{"className":1287},[1213]," 降至 ",[1099,1290,1292,1320],{"className":1291},[1102],[1099,1293,1295],{"className":1294},[1106],[1108,1296,1297],{"xmlns":1110},[1112,1298,1299,1317],{},[1115,1300,1301,1303,1305,1307,1310,1313,1315],{},[1118,1302,1120],{},[1122,1304,1125],{"stretchy":1124},[1118,1306,1131],{},[1118,1308,1309],{},"log",[1122,1311,1312],{},"⁡",[1118,1314,1131],{},[1122,1316,1138],{"stretchy":1124},[1140,1318,1319],{"encoding":1142},"O(N\\log N)",[1099,1321,1323],{"className":1322,"ariaHidden":1148},[1147],[1099,1324,1326,1330,1333,1336,1339,1344,1353,1356,1359],{"className":1325},[1152],[1099,1327],{"className":1328,"style":1329},[1156],"height:1em;vertical-align:-0.25em;",[1099,1331,1120],{"className":1332,"style":1163},[1161,1162],[1099,1334,1125],{"className":1335},[1167],[1099,1337,1131],{"className":1338,"style":1174},[1161,1162],[1099,1340],{"className":1341,"style":1343},[1342],"mspace","margin-right:0.1667em;",[1099,1345,1348,1349],{"className":1346},[1347],"mop","lo",[1099,1350,1352],{"style":1351},"margin-right:0.0139em;","g",[1099,1354],{"className":1355,"style":1343},[1342],[1099,1357,1131],{"className":1358,"style":1174},[1161,1162],[1099,1360,1138],{"className":1361},[1213],"。本文进一步给出同步网络假设下局部决策策略的收敛性定理与收敛时间上界,并在私有链与以太坊 Sepolia 测试网数据上完成实验验证。",[1091,1364,1366],{"id":1365},"一引言与问题背景","一、引言与问题背景",[1095,1368,1369,1370,1429],{},"在以比特币为代表的经典最长链共识中,链选择规则由中本聪在 2008 年的比特币白皮书中首次提出,其本质是 Nakamoto 共识的核心分叉选择规则(fork choice rule):在所有合法链中,节点始终选择自创世区块起累计工作量证明(cumulative proof-of-work)最多的一条,并在其上继续出块。由于比特币的难度调整机制使累计难度与链长度高度相关,该规则在多数时期近似等价于\"最长链\",故常被简称为最长链共识。一条链被判定为合法,要求其上每一区块均满足工作量证明难度、前向哈希正确指向父区块、区块内交易合法且时间戳合理;当节点面对多条合法链时,选取累计难度最大者,若两链累计难度相同则暂时并存,待下一区块产生后决出胜负。经过若干后续区块确认(比特币社区常用的经验值为 ",[1099,1371,1373,1394],{"className":1372},[1102],[1099,1374,1376],{"className":1375},[1106],[1108,1377,1378],{"xmlns":1110},[1112,1379,1380,1391],{},[1115,1381,1382,1385,1388],{},[1118,1383,1384],{},"k",[1122,1386,1387],{},"=",[1133,1389,1390],{},"6",[1140,1392,1393],{"encoding":1142},"k=6",[1099,1395,1397,1419],{"className":1396,"ariaHidden":1148},[1147],[1099,1398,1400,1404,1408,1412,1416],{"className":1399},[1152],[1099,1401],{"className":1402,"style":1403},[1156],"height:0.6944em;",[1099,1405,1384],{"className":1406,"style":1407},[1161,1162],"margin-right:0.0315em;",[1099,1409],{"className":1410,"style":1411},[1342],"margin-right:0.2778em;",[1099,1413,1387],{"className":1414},[1415],"mrel",[1099,1417],{"className":1418,"style":1411},[1342],[1099,1420,1422,1426],{"className":1421},[1152],[1099,1423],{"className":1424,"style":1425},[1156],"height:0.6444em;",[1099,1427,1390],{"className":1428},[1161],")之后,交易被逆转的概率已极低,可近似认为最终确定。",[1095,1431,1432,1433,1506,1507,1536],{},"经典共识的判断逻辑完全本地化,不依赖任何全局协调,而是依靠算力竞赛与信息传播自然收敛。然而,其信息传播主要依赖 gossip(流言传播)协议的变种:新区块产生后,节点尽可能快、尽可能广地转发给大部分乃至全部邻居,邻居再继续转发。这种\"有新区块即广播\"的推送模式虽然传播迅速,但通信量极大,总通信量接近 ",[1099,1434,1436,1459],{"className":1435},[1102],[1099,1437,1439],{"className":1438},[1106],[1108,1440,1441],{"xmlns":1110},[1112,1442,1443,1457],{},[1115,1444,1445,1447,1449,1455],{},[1118,1446,1120],{},[1122,1448,1125],{"stretchy":1124},[1127,1450,1451,1453],{},[1118,1452,1131],{},[1133,1454,1135],{},[1122,1456,1138],{"stretchy":1124},[1140,1458,1143],{"encoding":1142},[1099,1460,1462],{"className":1461,"ariaHidden":1148},[1147],[1099,1463,1465,1468,1471,1474,1503],{"className":1464},[1152],[1099,1466],{"className":1467,"style":1157},[1156],[1099,1469,1120],{"className":1470,"style":1163},[1161,1162],[1099,1472,1125],{"className":1473},[1167],[1099,1475,1477,1480],{"className":1476},[1161],[1099,1478,1131],{"className":1479,"style":1174},[1161,1162],[1099,1481,1483],{"className":1482},[1178],[1099,1484,1486],{"className":1485},[1182],[1099,1487,1489],{"className":1488},[1186],[1099,1490,1492],{"className":1491,"style":1191},[1190],[1099,1493,1494,1497],{"style":1194},[1099,1495],{"className":1496,"style":1199},[1198],[1099,1498,1500],{"className":1499},[1203,1204,1205,1206],[1099,1501,1135],{"className":1502},[1161,1206],[1099,1504,1138],{"className":1505},[1213]," 量级(",[1099,1508,1510,1523],{"className":1509},[1102],[1099,1511,1513],{"className":1512},[1106],[1108,1514,1515],{"xmlns":1110},[1112,1516,1517,1521],{},[1115,1518,1519],{},[1118,1520,1131],{},[1140,1522,1131],{"encoding":1142},[1099,1524,1526],{"className":1525,"ariaHidden":1148},[1147],[1099,1527,1529,1533],{"className":1528},[1152],[1099,1530],{"className":1531,"style":1532},[1156],"height:0.6833em;",[1099,1534,1131],{"className":1535,"style":1174},[1161,1162]," 为节点数),在网络规模扩大时构成显著的可扩展性瓶颈。本文正是针对这一瓶颈,在同步网络假设下重新设计链选择的通信模式与决策机制。",[1091,1538,1540],{"id":1539},"二系统模型与同步网络假设","二、系统模型与同步网络假设",[1095,1542,1543,1547,1548,1629,1630,1738,1739,1817,1818,2001,2002,2127,2128,2157,2158,2187,2188,2216,2217,2308,2309,2365],{},[1544,1545,1546],"strong",{},"网络模型。"," 将区块链共识网络建模为无向图 ",[1099,1549,1551,1581],{"className":1550},[1102],[1099,1552,1554],{"className":1553},[1106],[1108,1555,1556],{"xmlns":1110},[1112,1557,1558,1578],{},[1115,1559,1560,1563,1565,1567,1570,1573,1576],{},[1118,1561,1562],{},"G",[1122,1564,1387],{},[1122,1566,1125],{"stretchy":1124},[1118,1568,1569],{},"V",[1122,1571,1572],{"separator":1148},",",[1118,1574,1575],{},"E",[1122,1577,1138],{"stretchy":1124},[1140,1579,1580],{"encoding":1142},"G = (V, E)",[1099,1582,1584,1602],{"className":1583,"ariaHidden":1148},[1147],[1099,1585,1587,1590,1593,1596,1599],{"className":1586},[1152],[1099,1588],{"className":1589,"style":1532},[1156],[1099,1591,1562],{"className":1592},[1161,1162],[1099,1594],{"className":1595,"style":1411},[1342],[1099,1597,1387],{"className":1598},[1415],[1099,1600],{"className":1601,"style":1411},[1342],[1099,1603,1605,1608,1611,1615,1619,1622,1626],{"className":1604},[1152],[1099,1606],{"className":1607,"style":1329},[1156],[1099,1609,1125],{"className":1610},[1167],[1099,1612,1569],{"className":1613,"style":1614},[1161,1162],"margin-right:0.2222em;",[1099,1616,1572],{"className":1617},[1618],"mpunct",[1099,1620],{"className":1621,"style":1343},[1342],[1099,1623,1575],{"className":1624,"style":1625},[1161,1162],"margin-right:0.0576em;",[1099,1627,1138],{"className":1628},[1213],",其中 ",[1099,1631,1633,1671],{"className":1632},[1102],[1099,1634,1636],{"className":1635},[1106],[1108,1637,1638],{"xmlns":1110},[1112,1639,1640,1668],{},[1115,1641,1642,1644,1646,1649,1652,1654,1656,1658,1661,1663,1665],{},[1118,1643,1569],{},[1122,1645,1387],{},[1122,1647,1648],{"stretchy":1124},"{",[1133,1650,1651],{},"1",[1122,1653,1572],{"separator":1148},[1133,1655,1135],{},[1122,1657,1572],{"separator":1148},[1122,1659,1660],{},"…",[1122,1662,1572],{"separator":1148},[1118,1664,1131],{},[1122,1666,1667],{"stretchy":1124},"}",[1140,1669,1670],{"encoding":1142},"V = \\{1, 2, \\ldots, N\\}",[1099,1672,1674,1692],{"className":1673,"ariaHidden":1148},[1147],[1099,1675,1677,1680,1683,1686,1689],{"className":1676},[1152],[1099,1678],{"className":1679,"style":1532},[1156],[1099,1681,1569],{"className":1682,"style":1614},[1161,1162],[1099,1684],{"className":1685,"style":1411},[1342],[1099,1687,1387],{"className":1688},[1415],[1099,1690],{"className":1691,"style":1411},[1342],[1099,1693,1695,1698,1701,1704,1707,1710,1713,1716,1719,1723,1726,1729,1732,1735],{"className":1694},[1152],[1099,1696],{"className":1697,"style":1329},[1156],[1099,1699,1648],{"className":1700},[1167],[1099,1702,1651],{"className":1703},[1161],[1099,1705,1572],{"className":1706},[1618],[1099,1708],{"className":1709,"style":1343},[1342],[1099,1711,1135],{"className":1712},[1161],[1099,1714,1572],{"className":1715},[1618],[1099,1717],{"className":1718,"style":1343},[1342],[1099,1720,1660],{"className":1721},[1722],"minner",[1099,1724],{"className":1725,"style":1343},[1342],[1099,1727,1572],{"className":1728},[1618],[1099,1730],{"className":1731,"style":1343},[1342],[1099,1733,1131],{"className":1734,"style":1174},[1161,1162],[1099,1736,1667],{"className":1737},[1213]," 为共识节点集合,",[1099,1740,1742,1766],{"className":1741},[1102],[1099,1743,1745],{"className":1744},[1106],[1108,1746,1747],{"xmlns":1110},[1112,1748,1749,1763],{},[1115,1750,1751,1753,1756,1758,1761],{},[1118,1752,1575],{},[1122,1754,1755],{},"⊆",[1118,1757,1569],{},[1122,1759,1760],{},"×",[1118,1762,1569],{},[1140,1764,1765],{"encoding":1142},"E \\subseteq V \\times V",[1099,1767,1769,1788,1808],{"className":1768,"ariaHidden":1148},[1147],[1099,1770,1772,1776,1779,1782,1785],{"className":1771},[1152],[1099,1773],{"className":1774,"style":1775},[1156],"height:0.8193em;vertical-align:-0.136em;",[1099,1777,1575],{"className":1778,"style":1625},[1161,1162],[1099,1780],{"className":1781,"style":1411},[1342],[1099,1783,1755],{"className":1784},[1415],[1099,1786],{"className":1787,"style":1411},[1342],[1099,1789,1791,1795,1798,1801,1805],{"className":1790},[1152],[1099,1792],{"className":1793,"style":1794},[1156],"height:0.7667em;vertical-align:-0.0833em;",[1099,1796,1569],{"className":1797,"style":1614},[1161,1162],[1099,1799],{"className":1800,"style":1614},[1342],[1099,1802,1760],{"className":1803},[1804],"mbin",[1099,1806],{"className":1807,"style":1614},[1342],[1099,1809,1811,1814],{"className":1810},[1152],[1099,1812],{"className":1813,"style":1532},[1156],[1099,1815,1569],{"className":1816,"style":1614},[1161,1162]," 为节点间的连接集合。网络拓扑由邻接矩阵 ",[1099,1819,1821,1868],{"className":1820},[1102],[1099,1822,1824],{"className":1823},[1106],[1108,1825,1826],{"xmlns":1110},[1112,1827,1828,1865],{},[1115,1829,1830,1833,1835,1838,1852],{},[1118,1831,1832],{},"A",[1122,1834,1387],{},[1122,1836,1837],{"stretchy":1124},"[",[1839,1840,1841,1844],"msub",{},[1118,1842,1843],{},"a",[1115,1845,1846,1849],{},[1118,1847,1848],{},"i",[1118,1850,1851],{},"j",[1839,1853,1854,1857],{},[1122,1855,1856],{"stretchy":1124},"]",[1115,1858,1859,1861,1863],{},[1118,1860,1131],{},[1122,1862,1760],{},[1118,1864,1131],{},[1140,1866,1867],{"encoding":1142},"A = [a_{ij}]_{N \\times N}",[1099,1869,1871,1889],{"className":1870,"ariaHidden":1148},[1147],[1099,1872,1874,1877,1880,1883,1886],{"className":1873},[1152],[1099,1875],{"className":1876,"style":1532},[1156],[1099,1878,1832],{"className":1879},[1161,1162],[1099,1881],{"className":1882,"style":1411},[1342],[1099,1884,1387],{"className":1885},[1415],[1099,1887],{"className":1888,"style":1411},[1342],[1099,1890,1892,1896,1899,1950],{"className":1891},[1152],[1099,1893],{"className":1894,"style":1895},[1156],"height:1.0361em;vertical-align:-0.2861em;",[1099,1897,1837],{"className":1898},[1167],[1099,1900,1902,1905],{"className":1901},[1161],[1099,1903,1843],{"className":1904},[1161,1162],[1099,1906,1908],{"className":1907},[1178],[1099,1909,1912,1941],{"className":1910},[1182,1911],"vlist-t2",[1099,1913,1915,1936],{"className":1914},[1186],[1099,1916,1919],{"className":1917,"style":1918},[1190],"height:0.3117em;",[1099,1920,1922,1925],{"style":1921},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1099,1923],{"className":1924,"style":1199},[1198],[1099,1926,1928],{"className":1927},[1203,1204,1205,1206],[1099,1929,1931],{"className":1930},[1161,1206],[1099,1932,1935],{"className":1933,"style":1934},[1161,1162,1206],"margin-right:0.0572em;","ij",[1099,1937,1940],{"className":1938},[1939],"vlist-s","​",[1099,1942,1944],{"className":1943},[1186],[1099,1945,1948],{"className":1946,"style":1947},[1190],"height:0.2861em;",[1099,1949],{},[1099,1951,1953,1956],{"className":1952},[1213],[1099,1954,1856],{"className":1955},[1213],[1099,1957,1959],{"className":1958},[1178],[1099,1960,1962,1992],{"className":1961},[1182,1911],[1099,1963,1965,1989],{"className":1964},[1186],[1099,1966,1969],{"className":1967,"style":1968},[1190],"height:0.3283em;",[1099,1970,1971,1974],{"style":1921},[1099,1972],{"className":1973,"style":1199},[1198],[1099,1975,1977],{"className":1976},[1203,1204,1205,1206],[1099,1978,1980,1983,1986],{"className":1979},[1161,1206],[1099,1981,1131],{"className":1982,"style":1174},[1161,1162,1206],[1099,1984,1760],{"className":1985},[1804,1206],[1099,1987,1131],{"className":1988,"style":1174},[1161,1162,1206],[1099,1990,1940],{"className":1991},[1939],[1099,1993,1995],{"className":1994},[1186],[1099,1996,1999],{"className":1997,"style":1998},[1190],"height:0.2083em;",[1099,2000],{}," 描述,",[1099,2003,2005,2041],{"className":2004},[1102],[1099,2006,2008],{"className":2007},[1106],[1108,2009,2010],{"xmlns":1110},[1112,2011,2012,2038],{},[1115,2013,2014,2024,2027,2029,2032,2034,2036],{},[1839,2015,2016,2018],{},[1118,2017,1843],{},[1115,2019,2020,2022],{},[1118,2021,1848],{},[1118,2023,1851],{},[1122,2025,2026],{},"∈",[1122,2028,1648],{"stretchy":1124},[1133,2030,2031],{},"0",[1122,2033,1572],{"separator":1148},[1133,2035,1651],{},[1122,2037,1667],{"stretchy":1124},[1140,2039,2040],{"encoding":1142},"a_{ij} \\in \\{0, 1\\}",[1099,2042,2044,2103],{"className":2043,"ariaHidden":1148},[1147],[1099,2045,2047,2051,2094,2097,2100],{"className":2046},[1152],[1099,2048],{"className":2049,"style":2050},[1156],"height:0.8252em;vertical-align:-0.2861em;",[1099,2052,2054,2057],{"className":2053},[1161],[1099,2055,1843],{"className":2056},[1161,1162],[1099,2058,2060],{"className":2059},[1178],[1099,2061,2063,2086],{"className":2062},[1182,1911],[1099,2064,2066,2083],{"className":2065},[1186],[1099,2067,2069],{"className":2068,"style":1918},[1190],[1099,2070,2071,2074],{"style":1921},[1099,2072],{"className":2073,"style":1199},[1198],[1099,2075,2077],{"className":2076},[1203,1204,1205,1206],[1099,2078,2080],{"className":2079},[1161,1206],[1099,2081,1935],{"className":2082,"style":1934},[1161,1162,1206],[1099,2084,1940],{"className":2085},[1939],[1099,2087,2089],{"className":2088},[1186],[1099,2090,2092],{"className":2091,"style":1947},[1190],[1099,2093],{},[1099,2095],{"className":2096,"style":1411},[1342],[1099,2098,2026],{"className":2099},[1415],[1099,2101],{"className":2102,"style":1411},[1342],[1099,2104,2106,2109,2112,2115,2118,2121,2124],{"className":2105},[1152],[1099,2107],{"className":2108,"style":1329},[1156],[1099,2110,1648],{"className":2111},[1167],[1099,2113,2031],{"className":2114},[1161],[1099,2116,1572],{"className":2117},[1618],[1099,2119],{"className":2120,"style":1343},[1342],[1099,2122,1651],{"className":2123},[1161],[1099,2125,1667],{"className":2126},[1213]," 表示节点 ",[1099,2129,2131,2144],{"className":2130},[1102],[1099,2132,2134],{"className":2133},[1106],[1108,2135,2136],{"xmlns":1110},[1112,2137,2138,2142],{},[1115,2139,2140],{},[1118,2141,1848],{},[1140,2143,1848],{"encoding":1142},[1099,2145,2147],{"className":2146,"ariaHidden":1148},[1147],[1099,2148,2150,2154],{"className":2149},[1152],[1099,2151],{"className":2152,"style":2153},[1156],"height:0.6595em;",[1099,2155,1848],{"className":2156},[1161,1162]," 与节点 ",[1099,2159,2161,2174],{"className":2160},[1102],[1099,2162,2164],{"className":2163},[1106],[1108,2165,2166],{"xmlns":1110},[1112,2167,2168,2172],{},[1115,2169,2170],{},[1118,2171,1851],{},[1140,2173,1851],{"encoding":1142},[1099,2175,2177],{"className":2176,"ariaHidden":1148},[1147],[1099,2178,2180,2184],{"className":2179},[1152],[1099,2181],{"className":2182,"style":2183},[1156],"height:0.854em;vertical-align:-0.1944em;",[1099,2185,1851],{"className":2186,"style":1934},[1161,1162]," 是否相连。假设图 ",[1099,2189,2191,2204],{"className":2190},[1102],[1099,2192,2194],{"className":2193},[1106],[1108,2195,2196],{"xmlns":1110},[1112,2197,2198,2202],{},[1115,2199,2200],{},[1118,2201,1562],{},[1140,2203,1562],{"encoding":1142},[1099,2205,2207],{"className":2206,"ariaHidden":1148},[1147],[1099,2208,2210,2213],{"className":2209},[1152],[1099,2211],{"className":2212,"style":1532},[1156],[1099,2214,1562],{"className":2215},[1161,1162]," 连通,且每个节点的度数至少为 ",[1099,2218,2220,2242],{"className":2219},[1102],[1099,2221,2223],{"className":2222},[1106],[1108,2224,2225],{"xmlns":1110},[1112,2226,2227,2239],{},[1115,2228,2229],{},[1839,2230,2231,2234,2237],{},[1118,2232,2233],{},"d",[1118,2235,2236],{},"min",[1122,2238,1312],{},[1140,2240,2241],{"encoding":1142},"d_{\\min}",[1099,2243,2245],{"className":2244,"ariaHidden":1148},[1147],[1099,2246,2248,2252],{"className":2247},[1152],[1099,2249],{"className":2250,"style":2251},[1156],"height:0.8444em;vertical-align:-0.15em;",[1099,2253,2255,2258],{"className":2254},[1161],[1099,2256,2233],{"className":2257},[1161,1162],[1099,2259,2261],{"className":2260},[1178],[1099,2262,2264,2299],{"className":2263},[1182,1911],[1099,2265,2267,2296],{"className":2266},[1186],[1099,2268,2271],{"className":2269,"style":2270},[1190],"height:0.3175em;",[1099,2272,2273,2276],{"style":1921},[1099,2274],{"className":2275,"style":1199},[1198],[1099,2277,2279],{"className":2278},[1203,1204,1205,1206],[1099,2280,2282],{"className":2281},[1161,1206],[1099,2283,2285,2289,2292],{"className":2284},[1347,1206],[1099,2286,2288],{"className":2287},[1206],"m",[1099,2290,1848],{"className":2291},[1206],[1099,2293,2295],{"className":2294},[1206],"n",[1099,2297,1940],{"className":2298},[1939],[1099,2300,2302],{"className":2301},[1186],[1099,2303,2306],{"className":2304,"style":2305},[1190],"height:0.15em;",[1099,2307],{},";进一步假设拓扑稀疏,平均度数为 ",[1099,2310,2312,2336],{"className":2311},[1102],[1099,2313,2315],{"className":2314},[1106],[1108,2316,2317],{"xmlns":1110},[1112,2318,2319,2333],{},[1115,2320,2321,2323,2325,2327,2329,2331],{},[1118,2322,1120],{},[1122,2324,1125],{"stretchy":1124},[1118,2326,1309],{},[1122,2328,1312],{},[1118,2330,1131],{},[1122,2332,1138],{"stretchy":1124},[1140,2334,2335],{"encoding":1142},"O(\\log N)",[1099,2337,2339],{"className":2338,"ariaHidden":1148},[1147],[1099,2340,2342,2345,2348,2351,2356,2359,2362],{"className":2341},[1152],[1099,2343],{"className":2344,"style":1329},[1156],[1099,2346,1120],{"className":2347,"style":1163},[1161,1162],[1099,2349,1125],{"className":2350},[1167],[1099,2352,1348,2354],{"className":2353},[1347],[1099,2355,1352],{"style":1351},[1099,2357],{"className":2358,"style":1343},[1342],[1099,2360,1131],{"className":2361,"style":1174},[1161,1162],[1099,2363,1138],{"className":2364},[1213]," 量级。",[1095,2367,2368,2371,2372,2427,2428,2456,2457,2485,2486,2515,2516,2547,2548,2601,2602,2664],{},[1544,2369,2370],{},"同步网络假设。"," 本文的算法设计建立在以下三条同步性假设之上:其一,消息传递延迟有上界,即存在常数 ",[1099,2373,2375,2396],{"className":2374},[1102],[1099,2376,2378],{"className":2377},[1106],[1108,2379,2380],{"xmlns":1110},[1112,2381,2382,2393],{},[1115,2383,2384,2388,2391],{},[1118,2385,2387],{"mathvariant":2386},"normal","Δ",[1122,2389,2390],{},">",[1133,2392,2031],{},[1140,2394,2395],{"encoding":1142},"\\Delta > 0",[1099,2397,2399,2418],{"className":2398,"ariaHidden":1148},[1147],[1099,2400,2402,2406,2409,2412,2415],{"className":2401},[1152],[1099,2403],{"className":2404,"style":2405},[1156],"height:0.7224em;vertical-align:-0.0391em;",[1099,2407,2387],{"className":2408},[1161],[1099,2410],{"className":2411,"style":1411},[1342],[1099,2413,2390],{"className":2414},[1415],[1099,2416],{"className":2417,"style":1411},[1342],[1099,2419,2421,2424],{"className":2420},[1152],[1099,2422],{"className":2423,"style":1425},[1156],[1099,2425,2031],{"className":2426},[1161],",使任意消息自节点 ",[1099,2429,2431,2444],{"className":2430},[1102],[1099,2432,2434],{"className":2433},[1106],[1108,2435,2436],{"xmlns":1110},[1112,2437,2438,2442],{},[1115,2439,2440],{},[1118,2441,1848],{},[1140,2443,1848],{"encoding":1142},[1099,2445,2447],{"className":2446,"ariaHidden":1148},[1147],[1099,2448,2450,2453],{"className":2449},[1152],[1099,2451],{"className":2452,"style":2153},[1156],[1099,2454,1848],{"className":2455},[1161,1162]," 传至节点 ",[1099,2458,2460,2473],{"className":2459},[1102],[1099,2461,2463],{"className":2462},[1106],[1108,2464,2465],{"xmlns":1110},[1112,2466,2467,2471],{},[1115,2468,2469],{},[1118,2470,1851],{},[1140,2472,1851],{"encoding":1142},[1099,2474,2476],{"className":2475,"ariaHidden":1148},[1147],[1099,2477,2479,2482],{"className":2478},[1152],[1099,2480],{"className":2481,"style":2183},[1156],[1099,2483,1851],{"className":2484,"style":1934},[1161,1162]," 的延迟不超过 ",[1099,2487,2489,2503],{"className":2488},[1102],[1099,2490,2492],{"className":2491},[1106],[1108,2493,2494],{"xmlns":1110},[1112,2495,2496,2500],{},[1115,2497,2498],{},[1118,2499,2387],{"mathvariant":2386},[1140,2501,2502],{"encoding":1142},"\\Delta",[1099,2504,2506],{"className":2505,"ariaHidden":1148},[1147],[1099,2507,2509,2512],{"className":2508},[1152],[1099,2510],{"className":2511,"style":1532},[1156],[1099,2513,2387],{"className":2514},[1161],";其二,节点时钟同步,所有节点本地时钟的偏差不超过 ",[1099,2517,2519,2534],{"className":2518},[1102],[1099,2520,2522],{"className":2521},[1106],[1108,2523,2524],{"xmlns":1110},[1112,2525,2526,2531],{},[1115,2527,2528],{},[1118,2529,2530],{},"δ",[1140,2532,2533],{"encoding":1142},"\\delta",[1099,2535,2537],{"className":2536,"ariaHidden":1148},[1147],[1099,2538,2540,2543],{"className":2539},[1152],[1099,2541],{"className":2542,"style":1403},[1156],[1099,2544,2530],{"className":2545,"style":2546},[1161,1162],"margin-right:0.0379em;",",且 ",[1099,2549,2551,2570],{"className":2550},[1102],[1099,2552,2554],{"className":2553},[1106],[1108,2555,2556],{"xmlns":1110},[1112,2557,2558,2567],{},[1115,2559,2560,2562,2565],{},[1118,2561,2530],{},[1122,2563,2564],{},"≪",[1118,2566,2387],{"mathvariant":2386},[1140,2568,2569],{"encoding":1142},"\\delta \\ll \\Delta",[1099,2571,2573,2592],{"className":2572,"ariaHidden":1148},[1147],[1099,2574,2576,2580,2583,2586,2589],{"className":2575},[1152],[1099,2577],{"className":2578,"style":2579},[1156],"height:0.7335em;vertical-align:-0.0391em;",[1099,2581,2530],{"className":2582,"style":2546},[1161,1162],[1099,2584],{"className":2585,"style":1411},[1342],[1099,2587,2564],{"className":2588},[1415],[1099,2590],{"className":2591,"style":1411},[1342],[1099,2593,2595,2598],{"className":2594},[1152],[1099,2596],{"className":2597,"style":1532},[1156],[1099,2599,2387],{"className":2600},[1161],";其三,网络拓扑稳定,在共识过程中拓扑结构保持相对不变。此外,安全性分析假设诚实节点占绝大多数(典型阈值为 ",[1099,2603,2605,2631],{"className":2604},[1102],[1099,2606,2608],{"className":2607},[1106],[1108,2609,2610],{"xmlns":1110},[1112,2611,2612,2628],{},[1115,2613,2614,2617,2620,2623,2626],{},[1133,2615,2616],{},"50",[1118,2618,2619],{"mathvariant":2386},"%",[1122,2621,2622],{},"∼",[1133,2624,2625],{},"67",[1118,2627,2619],{"mathvariant":2386},[1140,2629,2630],{"encoding":1142},"50\\%\\sim 67\\%",[1099,2632,2634,2654],{"className":2633,"ariaHidden":1148},[1147],[1099,2635,2637,2641,2645,2648,2651],{"className":2636},[1152],[1099,2638],{"className":2639,"style":2640},[1156],"height:0.8056em;vertical-align:-0.0556em;",[1099,2642,2644],{"className":2643},[1161],"50%",[1099,2646],{"className":2647,"style":1411},[1342],[1099,2649,2622],{"className":2650},[1415],[1099,2652],{"className":2653,"style":1411},[1342],[1099,2655,2657,2660],{"className":2656},[1152],[1099,2658],{"className":2659,"style":2640},[1156],[1099,2661,2663],{"className":2662},[1161],"67%","),且客观上存在一条累计工作量或长度最长的诚实链。正是在延迟有界、时钟基本同步这一较强前提下,才有可能以远低于全网广播的通信开销实现最长链的可靠收敛。",[1091,2666,2668],{"id":2667},"三lclcs-算法设计","三、LCLCS 算法设计",[2670,2671,2673],"h3",{"id":2672},"_31-传播策略从主动推送到惰性拉取","3.1 传播策略:从主动推送到惰性拉取",[1095,2675,2676],{},"LCLCS 与经典 gossip 广播的根本差异在于传播范式的转变。经典方案是\"推送式(push)\"的:节点一旦产生或接收到新区块便主动向大量邻居转发。LCLCS 则采用\"拉取式(pull)+ 惰性同步(lazy synchronization)\"的范式,可概括为\"问—比—抄\"三步级联:",[1095,2678,2679,2680,2722],{},"第一,节点平时只与少数固定邻居维持稀疏连接(平均度数约为 ",[1099,2681,2683,2701],{"className":2682},[1102],[1099,2684,2686],{"className":2685},[1106],[1108,2687,2688],{"xmlns":1110},[1112,2689,2690,2698],{},[1115,2691,2692,2694,2696],{},[1118,2693,1309],{},[1122,2695,1312],{},[1118,2697,1131],{},[1140,2699,2700],{"encoding":1142},"\\log N",[1099,2702,2704],{"className":2703,"ariaHidden":1148},[1147],[1099,2705,2707,2711,2716,2719],{"className":2706},[1152],[1099,2708],{"className":2709,"style":2710},[1156],"height:0.8889em;vertical-align:-0.1944em;",[1099,2712,1348,2714],{"className":2713},[1347],[1099,2715,1352],{"style":1351},[1099,2717],{"className":2718,"style":1343},[1342],[1099,2720,1131],{"className":2721,"style":1174},[1161,1162],"),不承担全网转发义务。第二,节点并非\"有新区块即发\",而是周期性地主动向邻居查询其当前链的长度与权重,即\"问\"。第三,节点将邻居汇报的状态与本地链进行本地比较,即\"比\";仅当发现某邻居的链明显更优时,才向该邻居请求完整链数据,即\"抄\"(惰性同步)。其本地决策逻辑为:若本地链优于所有邻居,则认为自身可能已是全局最长链,不主动发送任何数据;若存在更优邻居,则立即\"认输\"并同步该邻居的链。如此,真正的优质链会像滚雪球一般,通过这种\"问—比—抄\"的级联方式逐层传开,而无谓的广播流量被消除。",[2670,2724,2726],{"id":2725},"_32-单节点执行流程","3.2 单节点执行流程",[1095,2728,2729],{},"每个节点独立、持续地执行以下循环,通常以固定时间片或事件驱动方式实现:",[2731,2732,2733,2740,2816,2941,2947],"ol",{},[2734,2735,2736,2739],"li",{},[1544,2737,2738],{},"区块产生与接收。"," 若本节点为出块者,在完成 PoW 后生成新区块并仅追加到本地链,而不立即广播;当接收到邻居应请求发来的区块或整条链时,对其区块格式、签名、工作量证明、时间戳与前向哈希等进行完整合法性验证,验证通过后将其接入本地链的适当位置。",[2734,2741,2742,2745,2746,2781,2782,2815],{},[1544,2743,2744],{},"周期性邻居状态查询(核心通信步骤)。"," 节点以固定频率(周期通常为数秒至数十秒,远长于出块间隔)向其全部直接邻居发送轻量查询消息,查询内容仅包含当前链高度 ",[1099,2747,2749,2765],{"className":2748},[1102],[1099,2750,2752],{"className":2751},[1106],[1108,2753,2754],{"xmlns":1110},[1112,2755,2756,2762],{},[1115,2757,2758],{},[2759,2760,2761],"mtext",{},"length",[1140,2763,2764],{"encoding":1142},"\\text{length}",[1099,2766,2768],{"className":2767,"ariaHidden":1148},[1147],[1099,2769,2771,2774],{"className":2770},[1152],[1099,2772],{"className":2773,"style":2710},[1156],[1099,2775,2778],{"className":2776},[1161,2777],"text",[1099,2779,2761],{"className":2780},[1161],"、当前链总权重 ",[1099,2783,2785,2800],{"className":2784},[1102],[1099,2786,2788],{"className":2787},[1106],[1108,2789,2790],{"xmlns":1110},[1112,2791,2792,2797],{},[1115,2793,2794],{},[2759,2795,2796],{},"weight",[1140,2798,2799],{"encoding":1142},"\\text{weight}",[1099,2801,2803],{"className":2802,"ariaHidden":1148},[1147],[1099,2804,2806,2809],{"className":2805},[1152],[1099,2807],{"className":2808,"style":2710},[1156],[1099,2810,2812],{"className":2811},[1161,2777],[1099,2813,2796],{"className":2814},[1161],",以及可选的链尖区块哈希。单次查询与响应通常仅数百字节,故此步骤通信量极小。",[2734,2817,2818,2821,2822,2853,2854,2885,2886],{},[1544,2819,2820],{},"本地最长链判断(纯本地计算)。"," 节点将本地链与刚收到的全部邻居状态按以下词典序(lexicographic order)优先级比较:首先比较链高度 ",[1099,2823,2825,2838],{"className":2824},[1102],[1099,2826,2828],{"className":2827},[1106],[1108,2829,2830],{"xmlns":1110},[1112,2831,2832,2836],{},[1115,2833,2834],{},[2759,2835,2761],{},[1140,2837,2764],{"encoding":1142},[1099,2839,2841],{"className":2840,"ariaHidden":1148},[1147],[1099,2842,2844,2847],{"className":2843},[1152],[1099,2845],{"className":2846,"style":2710},[1156],[1099,2848,2850],{"className":2849},[1161,2777],[1099,2851,2761],{"className":2852},[1161],",取大者优先;高度相同时比较链权重 ",[1099,2855,2857,2870],{"className":2856},[1102],[1099,2858,2860],{"className":2859},[1106],[1108,2861,2862],{"xmlns":1110},[1112,2863,2864,2868],{},[1115,2865,2866],{},[2759,2867,2796],{},[1140,2869,2799],{"encoding":1142},[1099,2871,2873],{"className":2872,"ariaHidden":1148},[1147],[1099,2874,2876,2879],{"className":2875},[1152],[1099,2877],{"className":2878,"style":2710},[1156],[1099,2880,2882],{"className":2881},[1161,2777],[1099,2883,2796],{"className":2884},[1161],",取大者优先;高度与权重均相同时保留当前链,或以链尖哈希、时间戳等次要规则打破平局。判断结果分为三类:",[2887,2888,2889,2905],"table",{},[2890,2891,2892],"thead",{},[2893,2894,2895,2899,2902],"tr",{},[2896,2897,2898],"th",{},"情况",[2896,2900,2901],{},"判断结果",[2896,2903,2904],{},"后续动作",[2906,2907,2908,2919,2930],"tbody",{},[2893,2909,2910,2913,2916],{},[2911,2912,1832],"td",{},[2911,2914,2915],{},"本地链 ≥ 所有邻居",[2911,2917,2918],{},"保持当前链,继续在本地链上工作",[2893,2920,2921,2924,2927],{},[2911,2922,2923],{},"B",[2911,2925,2926],{},"至少一个邻居链明显更优",[2911,2928,2929],{},"选择其中最优者(最高 height + weight)",[2893,2931,2932,2935,2938],{},[2911,2933,2934],{},"C",[2911,2936,2937],{},"平局(高度、权重均相同)",[2911,2939,2940],{},"保守策略,暂时保留本地链",[2734,2942,2943,2946],{},[1544,2944,2945],{},"惰性链同步(仅在情况 B 触发)。"," 仅当判定为情况 B 时,节点才向\"胜出\"邻居发起完整链同步请求;接收到完整链或缺失后缀后,验证整链合法性,通过则切换本地链(发生本地重组 reorg),失败则将该邻居标记为不可信,并可降低其信任度或断开连接。",[2734,2948,2949,2952],{},[1544,2950,2951],{},"持续挖矿与验证。"," 无论是否发生切换,节点始终在当前本地认为最优的链上继续验证交易、打包新区块(若处于出块轮次)并尝试 PoW 计算。",[2670,2954,2956],{"id":2955},"_33-系统层面的收敛过程","3.3 系统层面的收敛过程",[1095,2958,2959,2960,3058],{},"从宏观视角看,收敛过程可描述为一个正反馈级联:某诚实矿工挖出真正的最长(最重)区块后,该区块首先被高度落后的直接邻居通过查询发现;这些邻居在下一查询周期切换至新链;新链信息随即以级联方式沿邻居关系向外扩散。由于网络同步、拓扑连通且诚实节点占多数,最长链信息将在 ",[1099,2961,2963,2994],{"className":2962},[1102],[1099,2964,2966],{"className":2965},[1106],[1108,2967,2968],{"xmlns":1110},[1112,2969,2970,2991],{},[1115,2971,2972,2974,2976,2979,2981,2983,2986,2989],{},[1118,2973,1120],{},[1122,2975,1125],{"stretchy":1124},[2759,2977,2978],{},"网络直径",[1122,2980,1138],{"stretchy":1124},[1122,2982,1760],{},[2759,2984,2985],{},"查询周期",[1122,2987,2988],{},"+",[1118,2990,2387],{"mathvariant":2386},[1140,2992,2993],{"encoding":1142},"O(\\text{网络直径}) \\times \\text{查询周期} + \\Delta",[1099,2995,2997,3028,3049],{"className":2996,"ariaHidden":1148},[1147],[1099,2998,3000,3003,3006,3009,3016,3019,3022,3025],{"className":2999},[1152],[1099,3001],{"className":3002,"style":1329},[1156],[1099,3004,1120],{"className":3005,"style":1163},[1161,1162],[1099,3007,1125],{"className":3008},[1167],[1099,3010,3012],{"className":3011},[1161,2777],[1099,3013,2978],{"className":3014},[1161,3015],"cjk_fallback",[1099,3017,1138],{"className":3018},[1213],[1099,3020],{"className":3021,"style":1614},[1342],[1099,3023,1760],{"className":3024},[1804],[1099,3026],{"className":3027,"style":1614},[1342],[1099,3029,3031,3034,3040,3043,3046],{"className":3030},[1152],[1099,3032],{"className":3033,"style":1794},[1156],[1099,3035,3037],{"className":3036},[1161,2777],[1099,3038,2985],{"className":3039},[1161,3015],[1099,3041],{"className":3042,"style":1614},[1342],[1099,3044,2988],{"className":3045},[1804],[1099,3047],{"className":3048,"style":1614},[1342],[1099,3050,3052,3055],{"className":3051},[1152],[1099,3053],{"className":3054,"style":1532},[1156],[1099,3056,2387],{"className":3057},[1161]," 的时间内覆盖几乎所有诚实节点;一旦绝大多数诚实节点切换至同一链,新区块便绝大多数接续其上,形成正反馈,竞争链迅速失去竞争力,系统最终收敛。",[2670,3060,3062],{"id":3061},"_34-与经典-nakamoto-共识的判断机制对比","3.4 与经典 Nakamoto 共识的判断机制对比",[1095,3064,3065],{},"LCLCS 与经典共识的判断均为完全本地化,二者的本质差异在于比较对象的范围与判断的触发时机。",[2887,3067,3068,3090],{},[2890,3069,3070],{},[2893,3071,3072,3075,3078,3081,3084,3087],{},[2896,3073,3074],{},"共识类型",[2896,3076,3077],{},"判断是否完全本地",[2896,3079,3080],{},"比较对象范围",[2896,3082,3083],{},"触发时机",[2896,3085,3086],{},"是否需要全局信息",[2896,3088,3089],{},"通信复杂度",[2906,3091,3092,3185],{},[2893,3093,3094,3097,3100,3103,3106,3109],{},[2911,3095,3096],{},"经典 Nakamoto(比特币)",[2911,3098,3099],{},"是",[2911,3101,3102],{},"所有已接收到的竞争链",[2911,3104,3105],{},"收到\u002F产生新区块时",[2911,3107,3108],{},"间接需要(靠 gossip)",[2911,3110,3111,3112],{},"高,",[1099,3113,3115,3138],{"className":3114},[1102],[1099,3116,3118],{"className":3117},[1106],[1108,3119,3120],{"xmlns":1110},[1112,3121,3122,3136],{},[1115,3123,3124,3126,3128,3134],{},[1118,3125,1120],{},[1122,3127,1125],{"stretchy":1124},[1127,3129,3130,3132],{},[1118,3131,1131],{},[1133,3133,1135],{},[1122,3135,1138],{"stretchy":1124},[1140,3137,1143],{"encoding":1142},[1099,3139,3141],{"className":3140,"ariaHidden":1148},[1147],[1099,3142,3144,3147,3150,3153,3182],{"className":3143},[1152],[1099,3145],{"className":3146,"style":1157},[1156],[1099,3148,1120],{"className":3149,"style":1163},[1161,1162],[1099,3151,1125],{"className":3152},[1167],[1099,3154,3156,3159],{"className":3155},[1161],[1099,3157,1131],{"className":3158,"style":1174},[1161,1162],[1099,3160,3162],{"className":3161},[1178],[1099,3163,3165],{"className":3164},[1182],[1099,3166,3168],{"className":3167},[1186],[1099,3169,3171],{"className":3170,"style":1191},[1190],[1099,3172,3173,3176],{"style":1194},[1099,3174],{"className":3175,"style":1199},[1198],[1099,3177,3179],{"className":3178},[1203,1204,1205,1206],[1099,3180,1135],{"className":3181},[1161,1206],[1099,3183,1138],{"className":3184},[1213],[2893,3186,3187,3190,3192,3195,3198,3201],{},[2911,3188,3189],{},"LCLCS(低复杂度同步版)",[2911,3191,3099],{},[2911,3193,3194],{},"仅直接邻居当前状态",[2911,3196,3197],{},"周期性邻居查询响应到达时",[2911,3199,3200],{},"不需要全局视图",[2911,3202,3203,3204],{},"低,",[1099,3205,3207,3232],{"className":3206},[1102],[1099,3208,3210],{"className":3209},[1106],[1108,3211,3212],{"xmlns":1110},[1112,3213,3214,3230],{},[1115,3215,3216,3218,3220,3222,3224,3226,3228],{},[1118,3217,1120],{},[1122,3219,1125],{"stretchy":1124},[1118,3221,1131],{},[1118,3223,1309],{},[1122,3225,1312],{},[1118,3227,1131],{},[1122,3229,1138],{"stretchy":1124},[1140,3231,1319],{"encoding":1142},[1099,3233,3235],{"className":3234,"ariaHidden":1148},[1147],[1099,3236,3238,3241,3244,3247,3250,3253,3258,3261,3264],{"className":3237},[1152],[1099,3239],{"className":3240,"style":1329},[1156],[1099,3242,1120],{"className":3243,"style":1163},[1161,1162],[1099,3245,1125],{"className":3246},[1167],[1099,3248,1131],{"className":3249,"style":1174},[1161,1162],[1099,3251],{"className":3252,"style":1343},[1342],[1099,3254,1348,3256],{"className":3255},[1347],[1099,3257,1352],{"style":1351},[1099,3259],{"className":3260,"style":1343},[1342],[1099,3262,1131],{"className":3263,"style":1174},[1161,1162],[1099,3265,1138],{"className":3266},[1213],[1095,3268,3269],{},"可见,LCLCS 保留了本地决策这一核心特性,但将比较对象由\"全网已知的所有竞争链\"收缩为\"当前直接邻居汇报的状态\",从而大幅降低了信息收集成本。",[1091,3271,3273],{"id":3272},"四主要贡献","四、主要贡献",[2670,3275,3277],{"id":3276},"_41-将网络动力学理论引入最长链共识建模","4.1 将网络动力学理论引入最长链共识建模",[1095,3279,3280,3281,3368,3369,3457],{},"本文首次将网络动力学(network dynamics)的连续时间建模方法系统应用于最长链共识过程,把离散、事件驱动的区块传播与链选择抽象为连续的网络耦合动力学系统。具体地,构建了节点链长度 ",[1099,3282,3284,3310],{"className":3283},[1102],[1099,3285,3287],{"className":3286},[1106],[1108,3288,3289],{"xmlns":1110},[1112,3290,3291,3307],{},[1115,3292,3293,3300,3302,3305],{},[1839,3294,3295,3298],{},[1118,3296,3297],{},"L",[1118,3299,1848],{},[1122,3301,1125],{"stretchy":1124},[1118,3303,3304],{},"t",[1122,3306,1138],{"stretchy":1124},[1140,3308,3309],{"encoding":1142},"L_i(t)",[1099,3311,3313],{"className":3312,"ariaHidden":1148},[1147],[1099,3314,3316,3319,3359,3362,3365],{"className":3315},[1152],[1099,3317],{"className":3318,"style":1329},[1156],[1099,3320,3322,3325],{"className":3321},[1161],[1099,3323,3297],{"className":3324},[1161,1162],[1099,3326,3328],{"className":3327},[1178],[1099,3329,3331,3351],{"className":3330},[1182,1911],[1099,3332,3334,3348],{"className":3333},[1186],[1099,3335,3337],{"className":3336,"style":1918},[1190],[1099,3338,3339,3342],{"style":1921},[1099,3340],{"className":3341,"style":1199},[1198],[1099,3343,3345],{"className":3344},[1203,1204,1205,1206],[1099,3346,1848],{"className":3347},[1161,1162,1206],[1099,3349,1940],{"className":3350},[1939],[1099,3352,3354],{"className":3353},[1186],[1099,3355,3357],{"className":3356,"style":2305},[1190],[1099,3358],{},[1099,3360,1125],{"className":3361},[1167],[1099,3363,3304],{"className":3364},[1161,1162],[1099,3366,1138],{"className":3367},[1213]," 与链权重 ",[1099,3370,3372,3397],{"className":3371},[1102],[1099,3373,3375],{"className":3374},[1106],[1108,3376,3377],{"xmlns":1110},[1112,3378,3379,3394],{},[1115,3380,3381,3388,3390,3392],{},[1839,3382,3383,3386],{},[1118,3384,3385],{},"W",[1118,3387,1848],{},[1122,3389,1125],{"stretchy":1124},[1118,3391,3304],{},[1122,3393,1138],{"stretchy":1124},[1140,3395,3396],{"encoding":1142},"W_i(t)",[1099,3398,3400],{"className":3399,"ariaHidden":1148},[1147],[1099,3401,3403,3406,3448,3451,3454],{"className":3402},[1152],[1099,3404],{"className":3405,"style":1329},[1156],[1099,3407,3409,3413],{"className":3408},[1161],[1099,3410,3385],{"className":3411,"style":3412},[1161,1162],"margin-right:0.1389em;",[1099,3414,3416],{"className":3415},[1178],[1099,3417,3419,3440],{"className":3418},[1182,1911],[1099,3420,3422,3437],{"className":3421},[1186],[1099,3423,3425],{"className":3424,"style":1918},[1190],[1099,3426,3428,3431],{"style":3427},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1099,3429],{"className":3430,"style":1199},[1198],[1099,3432,3434],{"className":3433},[1203,1204,1205,1206],[1099,3435,1848],{"className":3436},[1161,1162,1206],[1099,3438,1940],{"className":3439},[1939],[1099,3441,3443],{"className":3442},[1186],[1099,3444,3446],{"className":3445,"style":2305},[1190],[1099,3447],{},[1099,3449,1125],{"className":3450},[1167],[1099,3452,3304],{"className":3453},[1161,1162],[1099,3455,1138],{"className":3456},[1213]," 的连续时间动力学方程,以刻画最长链信息如何通过局部交互向全网传播并趋同,为后续的收敛性分析与参数影响分析奠定了统一的数学框架。",[2670,3459,3461],{"id":3460},"_42-重构比较对象与触发时机","4.2 重构比较对象与触发时机",[1095,3463,3464,3465,3468,3469,3472],{},"在同步网络假设下,本文对经典最长链共识的两个关键决策维度进行了根本性调整。其一,",[1544,3466,3467],{},"缩小比较对象范围",":传统方式要求节点将本地链与已知的所有竞争链比较,依赖全网广播收集信息;改进方式则令节点仅与直接邻居的最新状态(链高度与链权重)比较,将比较范围由全网收缩为稀疏图中的邻居子集。其二,",[1544,3470,3471],{},"将触发时机由事件驱动改为周期驱动",":传统方式每收到或产生一个新区块即立即触发比较;改进方式则令节点以固定间隔主动向邻居发送轻量查询,收到响应后再进行比较与决策。二者共同作用,使通信开销显著下降。",[2670,3474,3476],{"id":3475},"_43-基于链权重的快速收敛机制","4.3 基于链权重的快速收敛机制",[1095,3478,3479],{},"为加速分叉解决与共识收敛,本文设计了多维度的区块权重计算方法:",[1095,3481,3482],{},[1099,3483,3485,3552],{"className":3484},[1102],[1099,3486,3488],{"className":3487},[1106],[1108,3489,3490],{"xmlns":1110},[1112,3491,3492,3549],{},[1115,3493,3494,3497,3499,3502,3504,3506,3513,3515,3517,3519,3521,3528,3530,3532,3534,3536,3543,3545,3547],{},[1118,3495,3496],{},"w",[1122,3498,1125],{"stretchy":1124},[1118,3500,3501],{},"b",[1122,3503,1138],{"stretchy":1124},[1122,3505,1387],{},[1839,3507,3508,3510],{},[1118,3509,3496],{},[2759,3511,3512],{},"work",[1122,3514,1125],{"stretchy":1124},[1118,3516,3501],{},[1122,3518,1138],{"stretchy":1124},[1122,3520,2988],{},[1839,3522,3523,3525],{},[1118,3524,3496],{},[2759,3526,3527],{},"time",[1122,3529,1125],{"stretchy":1124},[1118,3531,3501],{},[1122,3533,1138],{"stretchy":1124},[1122,3535,2988],{},[1839,3537,3538,3540],{},[1118,3539,3496],{},[2759,3541,3542],{},"priority",[1122,3544,1125],{"stretchy":1124},[1118,3546,3501],{},[1122,3548,1138],{"stretchy":1124},[1140,3550,3551],{"encoding":1142},"w(b) = w_{\\text{work}}(b) + w_{\\text{time}}(b) + w_{\\text{priority}}(b)",[1099,3553,3555,3583,3655,3725],{"className":3554,"ariaHidden":1148},[1147],[1099,3556,3558,3561,3565,3568,3571,3574,3577,3580],{"className":3557},[1152],[1099,3559],{"className":3560,"style":1329},[1156],[1099,3562,3496],{"className":3563,"style":3564},[1161,1162],"margin-right:0.0269em;",[1099,3566,1125],{"className":3567},[1167],[1099,3569,3501],{"className":3570},[1161,1162],[1099,3572,1138],{"className":3573},[1213],[1099,3575],{"className":3576,"style":1411},[1342],[1099,3578,1387],{"className":3579},[1415],[1099,3581],{"className":3582,"style":1411},[1342],[1099,3584,3586,3589,3637,3640,3643,3646,3649,3652],{"className":3585},[1152],[1099,3587],{"className":3588,"style":1329},[1156],[1099,3590,3592,3595],{"className":3591},[1161],[1099,3593,3496],{"className":3594,"style":3564},[1161,1162],[1099,3596,3598],{"className":3597},[1178],[1099,3599,3601,3629],{"className":3600},[1182,1911],[1099,3602,3604,3626],{"className":3603},[1186],[1099,3605,3608],{"className":3606,"style":3607},[1190],"height:0.3361em;",[1099,3609,3611,3614],{"style":3610},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1099,3612],{"className":3613,"style":1199},[1198],[1099,3615,3617],{"className":3616},[1203,1204,1205,1206],[1099,3618,3620],{"className":3619},[1161,1206],[1099,3621,3623],{"className":3622},[1161,2777,1206],[1099,3624,3512],{"className":3625},[1161,1206],[1099,3627,1940],{"className":3628},[1939],[1099,3630,3632],{"className":3631},[1186],[1099,3633,3635],{"className":3634,"style":2305},[1190],[1099,3636],{},[1099,3638,1125],{"className":3639},[1167],[1099,3641,3501],{"className":3642},[1161,1162],[1099,3644,1138],{"className":3645},[1213],[1099,3647],{"className":3648,"style":1614},[1342],[1099,3650,2988],{"className":3651},[1804],[1099,3653],{"className":3654,"style":1614},[1342],[1099,3656,3658,3661,3707,3710,3713,3716,3719,3722],{"className":3657},[1152],[1099,3659],{"className":3660,"style":1329},[1156],[1099,3662,3664,3667],{"className":3663},[1161],[1099,3665,3496],{"className":3666,"style":3564},[1161,1162],[1099,3668,3670],{"className":3669},[1178],[1099,3671,3673,3699],{"className":3672},[1182,1911],[1099,3674,3676,3696],{"className":3675},[1186],[1099,3677,3679],{"className":3678,"style":2270},[1190],[1099,3680,3681,3684],{"style":3610},[1099,3682],{"className":3683,"style":1199},[1198],[1099,3685,3687],{"className":3686},[1203,1204,1205,1206],[1099,3688,3690],{"className":3689},[1161,1206],[1099,3691,3693],{"className":3692},[1161,2777,1206],[1099,3694,3527],{"className":3695},[1161,1206],[1099,3697,1940],{"className":3698},[1939],[1099,3700,3702],{"className":3701},[1186],[1099,3703,3705],{"className":3704,"style":2305},[1190],[1099,3706],{},[1099,3708,1125],{"className":3709},[1167],[1099,3711,3501],{"className":3712},[1161,1162],[1099,3714,1138],{"className":3715},[1213],[1099,3717],{"className":3718,"style":1614},[1342],[1099,3720,2988],{"className":3721},[1804],[1099,3723],{"className":3724,"style":1614},[1342],[1099,3726,3728,3731,3777,3780,3783],{"className":3727},[1152],[1099,3729],{"className":3730,"style":1895},[1156],[1099,3732,3734,3737],{"className":3733},[1161],[1099,3735,3496],{"className":3736,"style":3564},[1161,1162],[1099,3738,3740],{"className":3739},[1178],[1099,3741,3743,3769],{"className":3742},[1182,1911],[1099,3744,3746,3766],{"className":3745},[1186],[1099,3747,3749],{"className":3748,"style":2270},[1190],[1099,3750,3751,3754],{"style":3610},[1099,3752],{"className":3753,"style":1199},[1198],[1099,3755,3757],{"className":3756},[1203,1204,1205,1206],[1099,3758,3760],{"className":3759},[1161,1206],[1099,3761,3763],{"className":3762},[1161,2777,1206],[1099,3764,3542],{"className":3765},[1161,1206],[1099,3767,1940],{"className":3768},[1939],[1099,3770,3772],{"className":3771},[1186],[1099,3773,3775],{"className":3774,"style":1947},[1190],[1099,3776],{},[1099,3778,1125],{"className":3779},[1167],[1099,3781,3501],{"className":3782},[1161,1162],[1099,3784,1138],{"className":3785},[1213],[1095,3787,3788,3789,3880,3881,3972,3973,4163,4164,4255],{},"其中 ",[1099,3790,3792,3816],{"className":3791},[1102],[1099,3793,3795],{"className":3794},[1106],[1108,3796,3797],{"xmlns":1110},[1112,3798,3799,3813],{},[1115,3800,3801,3807,3809,3811],{},[1839,3802,3803,3805],{},[1118,3804,3496],{},[2759,3806,3512],{},[1122,3808,1125],{"stretchy":1124},[1118,3810,3501],{},[1122,3812,1138],{"stretchy":1124},[1140,3814,3815],{"encoding":1142},"w_{\\text{work}}(b)",[1099,3817,3819],{"className":3818,"ariaHidden":1148},[1147],[1099,3820,3822,3825,3871,3874,3877],{"className":3821},[1152],[1099,3823],{"className":3824,"style":1329},[1156],[1099,3826,3828,3831],{"className":3827},[1161],[1099,3829,3496],{"className":3830,"style":3564},[1161,1162],[1099,3832,3834],{"className":3833},[1178],[1099,3835,3837,3863],{"className":3836},[1182,1911],[1099,3838,3840,3860],{"className":3839},[1186],[1099,3841,3843],{"className":3842,"style":3607},[1190],[1099,3844,3845,3848],{"style":3610},[1099,3846],{"className":3847,"style":1199},[1198],[1099,3849,3851],{"className":3850},[1203,1204,1205,1206],[1099,3852,3854],{"className":3853},[1161,1206],[1099,3855,3857],{"className":3856},[1161,2777,1206],[1099,3858,3512],{"className":3859},[1161,1206],[1099,3861,1940],{"className":3862},[1939],[1099,3864,3866],{"className":3865},[1186],[1099,3867,3869],{"className":3868,"style":2305},[1190],[1099,3870],{},[1099,3872,1125],{"className":3873},[1167],[1099,3875,3501],{"className":3876},[1161,1162],[1099,3878,1138],{"className":3879},[1213]," 为传统工作量权重(如 PoW 难度);",[1099,3882,3884,3908],{"className":3883},[1102],[1099,3885,3887],{"className":3886},[1106],[1108,3888,3889],{"xmlns":1110},[1112,3890,3891,3905],{},[1115,3892,3893,3899,3901,3903],{},[1839,3894,3895,3897],{},[1118,3896,3496],{},[2759,3898,3527],{},[1122,3900,1125],{"stretchy":1124},[1118,3902,3501],{},[1122,3904,1138],{"stretchy":1124},[1140,3906,3907],{"encoding":1142},"w_{\\text{time}}(b)",[1099,3909,3911],{"className":3910,"ariaHidden":1148},[1147],[1099,3912,3914,3917,3963,3966,3969],{"className":3913},[1152],[1099,3915],{"className":3916,"style":1329},[1156],[1099,3918,3920,3923],{"className":3919},[1161],[1099,3921,3496],{"className":3922,"style":3564},[1161,1162],[1099,3924,3926],{"className":3925},[1178],[1099,3927,3929,3955],{"className":3928},[1182,1911],[1099,3930,3932,3952],{"className":3931},[1186],[1099,3933,3935],{"className":3934,"style":2270},[1190],[1099,3936,3937,3940],{"style":3610},[1099,3938],{"className":3939,"style":1199},[1198],[1099,3941,3943],{"className":3942},[1203,1204,1205,1206],[1099,3944,3946],{"className":3945},[1161,1206],[1099,3947,3949],{"className":3948},[1161,2777,1206],[1099,3950,3527],{"className":3951},[1161,1206],[1099,3953,1940],{"className":3954},[1939],[1099,3956,3958],{"className":3957},[1186],[1099,3959,3961],{"className":3960,"style":2305},[1190],[1099,3962],{},[1099,3964,1125],{"className":3965},[1167],[1099,3967,3501],{"className":3968},[1161,1162],[1099,3970,1138],{"className":3971},[1213]," 为时间衰减权重,采用指数衰减形式 ",[1099,3974,3976,4027],{"className":3975},[1102],[1099,3977,3979],{"className":3978},[1106],[1108,3980,3981],{"xmlns":1110},[1112,3982,3983,4024],{},[1115,3984,3985,3988,3991,3994,3996,3999,4002,4005,4008,4010,4012,4014,4020,4022],{},[1118,3986,3987],{},"α",[1122,3989,3990],{},"⋅",[1118,3992,3993],{},"exp",[1122,3995,1312],{},[2759,3997,3998],{}," ⁣",[1122,4000,1125],{"fence":1124,"stretchy":1148,"minsize":4001,"maxsize":4001},"1.2em",[1122,4003,4004],{},"−",[1118,4006,4007],{},"λ",[1122,4009,1125],{"stretchy":1124},[1118,4011,3304],{},[1122,4013,4004],{},[1839,4015,4016,4018],{},[1118,4017,3304],{},[1118,4019,3501],{},[1122,4021,1138],{"stretchy":1124},[1122,4023,1138],{"fence":1124,"stretchy":1148,"minsize":4001,"maxsize":4001},[1140,4025,4026],{"encoding":1142},"\\alpha \\cdot \\exp\\!\\big(-\\lambda (t - t_b)\\big)",[1099,4028,4030,4050,4084,4108],{"className":4029,"ariaHidden":1148},[1147],[1099,4031,4033,4037,4041,4044,4047],{"className":4032},[1152],[1099,4034],{"className":4035,"style":4036},[1156],"height:0.4445em;",[1099,4038,3987],{"className":4039,"style":4040},[1161,1162],"margin-right:0.0037em;",[1099,4042],{"className":4043,"style":1614},[1342],[1099,4045,3990],{"className":4046},[1804],[1099,4048],{"className":4049,"style":1614},[1342],[1099,4051,4053,4057,4060,4064,4067,4075,4078,4081],{"className":4052},[1152],[1099,4054],{"className":4055,"style":4056},[1156],"height:1.2em;vertical-align:-0.35em;",[1099,4058,3993],{"className":4059},[1347],[1099,4061],{"className":4062,"style":4063},[1342],"margin-right:-0.1667em;",[1099,4065],{"className":4066,"style":1343},[1342],[1099,4068,4070],{"className":4069},[1161],[1099,4071,1125],{"className":4072},[4073,4074],"delimsizing","size1",[1099,4076],{"className":4077,"style":1614},[1342],[1099,4079,4004],{"className":4080},[1804],[1099,4082],{"className":4083,"style":1614},[1342],[1099,4085,4087,4090,4093,4096,4099,4102,4105],{"className":4086},[1152],[1099,4088],{"className":4089,"style":1329},[1156],[1099,4091,4007],{"className":4092},[1161,1162],[1099,4094,1125],{"className":4095},[1167],[1099,4097,3304],{"className":4098},[1161,1162],[1099,4100],{"className":4101,"style":1614},[1342],[1099,4103,4004],{"className":4104},[1804],[1099,4106],{"className":4107,"style":1614},[1342],[1099,4109,4111,4114,4154,4157],{"className":4110},[1152],[1099,4112],{"className":4113,"style":4056},[1156],[1099,4115,4117,4120],{"className":4116},[1161],[1099,4118,3304],{"className":4119},[1161,1162],[1099,4121,4123],{"className":4122},[1178],[1099,4124,4126,4146],{"className":4125},[1182,1911],[1099,4127,4129,4143],{"className":4128},[1186],[1099,4130,4132],{"className":4131,"style":3607},[1190],[1099,4133,4134,4137],{"style":1921},[1099,4135],{"className":4136,"style":1199},[1198],[1099,4138,4140],{"className":4139},[1203,1204,1205,1206],[1099,4141,3501],{"className":4142},[1161,1162,1206],[1099,4144,1940],{"className":4145},[1939],[1099,4147,4149],{"className":4148},[1186],[1099,4150,4152],{"className":4151,"style":2305},[1190],[1099,4153],{},[1099,4155,1138],{"className":4156},[1213],[1099,4158,4160],{"className":4159},[1161],[1099,4161,1138],{"className":4162},[4073,4074],",使较早区块获得更高权重;",[1099,4165,4167,4191],{"className":4166},[1102],[1099,4168,4170],{"className":4169},[1106],[1108,4171,4172],{"xmlns":1110},[1112,4173,4174,4188],{},[1115,4175,4176,4182,4184,4186],{},[1839,4177,4178,4180],{},[1118,4179,3496],{},[2759,4181,3542],{},[1122,4183,1125],{"stretchy":1124},[1118,4185,3501],{},[1122,4187,1138],{"stretchy":1124},[1140,4189,4190],{"encoding":1142},"w_{\\text{priority}}(b)",[1099,4192,4194],{"className":4193,"ariaHidden":1148},[1147],[1099,4195,4197,4200,4246,4249,4252],{"className":4196},[1152],[1099,4198],{"className":4199,"style":1895},[1156],[1099,4201,4203,4206],{"className":4202},[1161],[1099,4204,3496],{"className":4205,"style":3564},[1161,1162],[1099,4207,4209],{"className":4208},[1178],[1099,4210,4212,4238],{"className":4211},[1182,1911],[1099,4213,4215,4235],{"className":4214},[1186],[1099,4216,4218],{"className":4217,"style":2270},[1190],[1099,4219,4220,4223],{"style":3610},[1099,4221],{"className":4222,"style":1199},[1198],[1099,4224,4226],{"className":4225},[1203,1204,1205,1206],[1099,4227,4229],{"className":4228},[1161,1206],[1099,4230,4232],{"className":4231},[1161,2777,1206],[1099,4233,3542],{"className":4234},[1161,1206],[1099,4236,1940],{"className":4237},[1939],[1099,4239,4241],{"className":4240},[1186],[1099,4242,4244],{"className":4243,"style":1947},[1190],[1099,4245],{},[1099,4247,1125],{"className":4248},[1167],[1099,4250,3501],{"className":4251},[1161,1162],[1099,4253,1138],{"className":4254},[1213]," 为可选的优先级权重,可依交易重要性等设定。在此基础上建立加权最长链选择规则:优先选择链长度最大者,长度相同时选择总权重最大者,并通过权重耦合项增强动力学模型中权重信息的传播效率。",[2670,4257,4259],{"id":4258},"_44-收敛性分析与实验验证","4.4 收敛性分析与实验验证",[1095,4261,4262,4265,4266,1629,4342,4370,4371,4399,4400,1288,4473,4536],{},[1544,4263,4264],{},"理论方面",",本文给出了同步网络下局部决策策略的收敛性定理,并证明其收敛时间存在上界 ",[1099,4267,4269,4294],{"className":4268},[1102],[1099,4270,4272],{"className":4271},[1106],[1108,4273,4274],{"xmlns":1110},[1112,4275,4276,4291],{},[1115,4277,4278,4281,4284,4287,4289],{},[1118,4279,4280],{},"T",[1122,4282,4283],{},"≤",[1118,4285,4286],{},"D",[1122,4288,3990],{},[1118,4290,2387],{"mathvariant":2386},[1140,4292,4293],{"encoding":1142},"T \\le D \\cdot \\Delta",[1099,4295,4297,4315,4333],{"className":4296,"ariaHidden":1148},[1147],[1099,4298,4300,4303,4306,4309,4312],{"className":4299},[1152],[1099,4301],{"className":4302,"style":1775},[1156],[1099,4304,4280],{"className":4305,"style":3412},[1161,1162],[1099,4307],{"className":4308,"style":1411},[1342],[1099,4310,4283],{"className":4311},[1415],[1099,4313],{"className":4314,"style":1411},[1342],[1099,4316,4318,4321,4324,4327,4330],{"className":4317},[1152],[1099,4319],{"className":4320,"style":1532},[1156],[1099,4322,4286],{"className":4323,"style":1163},[1161,1162],[1099,4325],{"className":4326,"style":1614},[1342],[1099,4328,3990],{"className":4329},[1804],[1099,4331],{"className":4332,"style":1614},[1342],[1099,4334,4336,4339],{"className":4335},[1152],[1099,4337],{"className":4338,"style":1532},[1156],[1099,4340,2387],{"className":4341},[1161],[1099,4343,4345,4358],{"className":4344},[1102],[1099,4346,4348],{"className":4347},[1106],[1108,4349,4350],{"xmlns":1110},[1112,4351,4352,4356],{},[1115,4353,4354],{},[1118,4355,4286],{},[1140,4357,4286],{"encoding":1142},[1099,4359,4361],{"className":4360,"ariaHidden":1148},[1147],[1099,4362,4364,4367],{"className":4363},[1152],[1099,4365],{"className":4366,"style":1532},[1156],[1099,4368,4286],{"className":4369,"style":1163},[1161,1162]," 为网络直径、",[1099,4372,4374,4387],{"className":4373},[1102],[1099,4375,4377],{"className":4376},[1106],[1108,4378,4379],{"xmlns":1110},[1112,4380,4381,4385],{},[1115,4382,4383],{},[1118,4384,2387],{"mathvariant":2386},[1140,4386,2502],{"encoding":1142},[1099,4388,4390],{"className":4389,"ariaHidden":1148},[1147],[1099,4391,4393,4396],{"className":4392},[1152],[1099,4394],{"className":4395,"style":1532},[1156],[1099,4397,2387],{"className":4398},[1161]," 为消息延迟上界;同时论证了通信复杂度由传统的 ",[1099,4401,4403,4426],{"className":4402},[1102],[1099,4404,4406],{"className":4405},[1106],[1108,4407,4408],{"xmlns":1110},[1112,4409,4410,4424],{},[1115,4411,4412,4414,4416,4422],{},[1118,4413,1120],{},[1122,4415,1125],{"stretchy":1124},[1127,4417,4418,4420],{},[1118,4419,1131],{},[1133,4421,1135],{},[1122,4423,1138],{"stretchy":1124},[1140,4425,1143],{"encoding":1142},[1099,4427,4429],{"className":4428,"ariaHidden":1148},[1147],[1099,4430,4432,4435,4438,4441,4470],{"className":4431},[1152],[1099,4433],{"className":4434,"style":1157},[1156],[1099,4436,1120],{"className":4437,"style":1163},[1161,1162],[1099,4439,1125],{"className":4440},[1167],[1099,4442,4444,4447],{"className":4443},[1161],[1099,4445,1131],{"className":4446,"style":1174},[1161,1162],[1099,4448,4450],{"className":4449},[1178],[1099,4451,4453],{"className":4452},[1182],[1099,4454,4456],{"className":4455},[1186],[1099,4457,4459],{"className":4458,"style":1191},[1190],[1099,4460,4461,4464],{"style":1194},[1099,4462],{"className":4463,"style":1199},[1198],[1099,4465,4467],{"className":4466},[1203,1204,1205,1206],[1099,4468,1135],{"className":4469},[1161,1206],[1099,4471,1138],{"className":4472},[1213],[1099,4474,4476,4501],{"className":4475},[1102],[1099,4477,4479],{"className":4478},[1106],[1108,4480,4481],{"xmlns":1110},[1112,4482,4483,4499],{},[1115,4484,4485,4487,4489,4491,4493,4495,4497],{},[1118,4486,1120],{},[1122,4488,1125],{"stretchy":1124},[1118,4490,1131],{},[1118,4492,1309],{},[1122,4494,1312],{},[1118,4496,1131],{},[1122,4498,1138],{"stretchy":1124},[1140,4500,1319],{"encoding":1142},[1099,4502,4504],{"className":4503,"ariaHidden":1148},[1147],[1099,4505,4507,4510,4513,4516,4519,4522,4527,4530,4533],{"className":4506},[1152],[1099,4508],{"className":4509,"style":1329},[1156],[1099,4511,1120],{"className":4512,"style":1163},[1161,1162],[1099,4514,1125],{"className":4515},[1167],[1099,4517,1131],{"className":4518,"style":1174},[1161,1162],[1099,4520],{"className":4521,"style":1343},[1342],[1099,4523,1348,4525],{"className":4524},[1347],[1099,4526,1352],{"style":1351},[1099,4528],{"className":4529,"style":1343},[1342],[1099,4531,1131],{"className":4532,"style":1174},[1161,1162],[1099,4534,1138],{"className":4535},[1213],",且保持了最长链规则的基本安全性。",[1095,4538,4539,4542],{},[1544,4540,4541],{},"实验方面",",实验环境为 100 节点私有链并结合以太坊 Sepolia 测试网真实数据,对比对象为传统 PoW 与 GHOST 协议。结果表明:在 100 节点规模下通信开销降低约 92%;最长链收敛时间缩短 40% 以上;权重机制显著减少分叉次数,提升了链的稳定性。",[1091,4544,4546],{"id":4545},"五向异步网络的扩展","五、向异步网络的扩展",[1095,4548,4549],{},"上述同步版本在延迟有界、时钟同步的较强假设下实现了确定性的优越性能。为适配真实网络中更普遍的异步场景(延迟无界、时钟不同步、消息乱序或丢失),本文进一步给出异步扩展。",[1095,4551,4552,4555,4556,4648,4649,4744],{},[1544,4553,4554],{},"建模层面",",将网络动力学建模首次系统应用于异步条件下的最长链共识,建立引入概率传递项 ",[1099,4557,4559,4587],{"className":4558},[1102],[1099,4560,4562],{"className":4561},[1106],[1108,4563,4564],{"xmlns":1110},[1112,4565,4566,4584],{},[1115,4567,4568,4578,4580,4582],{},[1839,4569,4570,4572],{},[1118,4571,1095],{},[1115,4573,4574,4576],{},[1118,4575,1848],{},[1118,4577,1851],{},[1122,4579,1125],{"stretchy":1124},[1118,4581,3304],{},[1122,4583,1138],{"stretchy":1124},[1140,4585,4586],{"encoding":1142},"p_{ij}(t)",[1099,4588,4590],{"className":4589,"ariaHidden":1148},[1147],[1099,4591,4593,4596,4639,4642,4645],{"className":4592},[1152],[1099,4594],{"className":4595,"style":1895},[1156],[1099,4597,4599,4602],{"className":4598},[1161],[1099,4600,1095],{"className":4601},[1161,1162],[1099,4603,4605],{"className":4604},[1178],[1099,4606,4608,4631],{"className":4607},[1182,1911],[1099,4609,4611,4628],{"className":4610},[1186],[1099,4612,4614],{"className":4613,"style":1918},[1190],[1099,4615,4616,4619],{"style":1921},[1099,4617],{"className":4618,"style":1199},[1198],[1099,4620,4622],{"className":4621},[1203,1204,1205,1206],[1099,4623,4625],{"className":4624},[1161,1206],[1099,4626,1935],{"className":4627,"style":1934},[1161,1162,1206],[1099,4629,1940],{"className":4630},[1939],[1099,4632,4634],{"className":4633},[1186],[1099,4635,4637],{"className":4636,"style":1947},[1190],[1099,4638],{},[1099,4640,1125],{"className":4641},[1167],[1099,4643,3304],{"className":4644},[1161,1162],[1099,4646,1138],{"className":4647},[1213]," 与随机延迟 ",[1099,4650,4652,4681],{"className":4651},[1102],[1099,4653,4655],{"className":4654},[1106],[1108,4656,4657],{"xmlns":1110},[1112,4658,4659,4678],{},[1115,4660,4661,4672,4674,4676],{},[1839,4662,4663,4666],{},[1118,4664,4665],{},"τ",[1115,4667,4668,4670],{},[1118,4669,1848],{},[1118,4671,1851],{},[1122,4673,1125],{"stretchy":1124},[1118,4675,3304],{},[1122,4677,1138],{"stretchy":1124},[1140,4679,4680],{"encoding":1142},"\\tau_{ij}(t)",[1099,4682,4684],{"className":4683,"ariaHidden":1148},[1147],[1099,4685,4687,4690,4735,4738,4741],{"className":4686},[1152],[1099,4688],{"className":4689,"style":1895},[1156],[1099,4691,4693,4697],{"className":4692},[1161],[1099,4694,4665],{"className":4695,"style":4696},[1161,1162],"margin-right:0.1132em;",[1099,4698,4700],{"className":4699},[1178],[1099,4701,4703,4727],{"className":4702},[1182,1911],[1099,4704,4706,4724],{"className":4705},[1186],[1099,4707,4709],{"className":4708,"style":1918},[1190],[1099,4710,4712,4715],{"style":4711},"top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;",[1099,4713],{"className":4714,"style":1199},[1198],[1099,4716,4718],{"className":4717},[1203,1204,1205,1206],[1099,4719,4721],{"className":4720},[1161,1206],[1099,4722,1935],{"className":4723,"style":1934},[1161,1162,1206],[1099,4725,1940],{"className":4726},[1939],[1099,4728,4730],{"className":4729},[1186],[1099,4731,4733],{"className":4732,"style":1947},[1190],[1099,4734],{},[1099,4736,1125],{"className":4737},[1167],[1099,4739,3304],{"className":4740},[1161,1162],[1099,4742,1138],{"className":4743},[1213]," 的链长度动力学方程:",[1095,4746,4747],{},[1099,4748,4750,4864],{"className":4749},[1102],[1099,4751,4753],{"className":4752},[1106],[1108,4754,4755],{"xmlns":1110},[1112,4756,4757,4861],{},[1115,4758,4759,4784,4786,4792,4794,4796,4798,4800,4803,4810,4820,4822,4824,4826,4828,4831,4833,4835,4837,4839,4841,4844,4846,4848,4855,4857,4859],{},[4760,4761,4762,4778],"mfrac",{},[1115,4763,4764,4766,4772,4774,4776],{},[1118,4765,2233],{},[1839,4767,4768,4770],{},[1118,4769,3297],{},[1118,4771,1848],{},[1122,4773,1125],{"stretchy":1124},[1118,4775,3304],{},[1122,4777,1138],{"stretchy":1124},[1115,4779,4780,4782],{},[1118,4781,2233],{},[1118,4783,3304],{},[1122,4785,1387],{},[1839,4787,4788,4790],{},[1118,4789,3987],{},[1118,4791,1848],{},[1122,4793,1125],{"stretchy":1124},[1118,4795,3304],{},[1122,4797,1138],{"stretchy":1124},[1122,4799,2988],{},[1118,4801,4802],{},"β",[1839,4804,4805,4808],{},[1122,4806,4807],{},"∑",[1118,4809,1851],{},[1839,4811,4812,4814],{},[1118,4813,1095],{},[1115,4815,4816,4818],{},[1118,4817,1848],{},[1118,4819,1851],{},[1122,4821,1125],{"stretchy":1124},[1118,4823,3304],{},[1122,4825,1138],{"stretchy":1124},[1122,4827,3990],{},[1118,4829,4830],{},"max",[1122,4832,1312],{},[2759,4834,3998],{},[1122,4836,1125],{"fence":1124,"stretchy":1148,"minsize":4001,"maxsize":4001},[1133,4838,2031],{},[1122,4840,1572],{"separator":1148},[2759,4842,4843],{}," 延迟接收的邻居长度差",[1122,4845,1138],{"fence":1124,"stretchy":1148,"minsize":4001,"maxsize":4001},[1122,4847,2988],{},[1839,4849,4850,4853],{},[1118,4851,4852],{},"ξ",[1118,4854,1848],{},[1122,4856,1125],{"stretchy":1124},[1118,4858,3304],{},[1122,4860,1138],{"stretchy":1124},[1140,4862,4863],{"encoding":1142},"\\frac{dL_i(t)}{dt} = \\alpha_i(t) + \\beta \\sum_{j} p_{ij}(t)\\cdot \\max\\!\\big(0,\\ \\text{延迟接收的邻居长度差}\\big) + \\xi_i(t)",[1099,4865,4867,5017,5082,5209,5265],{"className":4866,"ariaHidden":1148},[1147],[1099,4868,4870,4874,5008,5011,5014],{"className":4869},[1152],[1099,4871],{"className":4872,"style":4873},[1156],"height:1.355em;vertical-align:-0.345em;",[1099,4875,4877,4881,5005],{"className":4876},[1161],[1099,4878],{"className":4879},[1167,4880],"nulldelimiter",[1099,4882,4884],{"className":4883},[4760],[1099,4885,4887,4996],{"className":4886},[1182,1911],[1099,4888,4890,4993],{"className":4889},[1186],[1099,4891,4894,4913,4924],{"className":4892,"style":4893},[1190],"height:1.01em;",[1099,4895,4897,4901],{"style":4896},"top:-2.655em;",[1099,4898],{"className":4899,"style":4900},[1198],"height:3em;",[1099,4902,4904],{"className":4903},[1203,1204,1205,1206],[1099,4905,4907,4910],{"className":4906},[1161,1206],[1099,4908,2233],{"className":4909},[1161,1162,1206],[1099,4911,3304],{"className":4912},[1161,1162,1206],[1099,4914,4916,4919],{"style":4915},"top:-3.23em;",[1099,4917],{"className":4918,"style":4900},[1198],[1099,4920],{"className":4921,"style":4923},[4922],"frac-line","border-bottom-width:0.04em;",[1099,4925,4927,4930],{"style":4926},"top:-3.485em;",[1099,4928],{"className":4929,"style":4900},[1198],[1099,4931,4933],{"className":4932},[1203,1204,1205,1206],[1099,4934,4936,4939,4984,4987,4990],{"className":4935},[1161,1206],[1099,4937,2233],{"className":4938},[1161,1162,1206],[1099,4940,4942,4945],{"className":4941},[1161,1206],[1099,4943,3297],{"className":4944},[1161,1162,1206],[1099,4946,4948],{"className":4947},[1178],[1099,4949,4951,4975],{"className":4950},[1182,1911],[1099,4952,4954,4972],{"className":4953},[1186],[1099,4955,4958],{"className":4956,"style":4957},[1190],"height:0.3281em;",[1099,4959,4961,4965],{"style":4960},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1099,4962],{"className":4963,"style":4964},[1198],"height:2.5em;",[1099,4966,4969],{"className":4967},[1203,4968,4074,1206],"reset-size3",[1099,4970,1848],{"className":4971},[1161,1162,1206],[1099,4973,1940],{"className":4974},[1939],[1099,4976,4978],{"className":4977},[1186],[1099,4979,4982],{"className":4980,"style":4981},[1190],"height:0.143em;",[1099,4983],{},[1099,4985,1125],{"className":4986},[1167,1206],[1099,4988,3304],{"className":4989},[1161,1162,1206],[1099,4991,1138],{"className":4992},[1213,1206],[1099,4994,1940],{"className":4995},[1939],[1099,4997,4999],{"className":4998},[1186],[1099,5000,5003],{"className":5001,"style":5002},[1190],"height:0.345em;",[1099,5004],{},[1099,5006],{"className":5007},[1213,4880],[1099,5009],{"className":5010,"style":1411},[1342],[1099,5012,1387],{"className":5013},[1415],[1099,5015],{"className":5016,"style":1411},[1342],[1099,5018,5020,5023,5064,5067,5070,5073,5076,5079],{"className":5019},[1152],[1099,5021],{"className":5022,"style":1329},[1156],[1099,5024,5026,5029],{"className":5025},[1161],[1099,5027,3987],{"className":5028,"style":4040},[1161,1162],[1099,5030,5032],{"className":5031},[1178],[1099,5033,5035,5056],{"className":5034},[1182,1911],[1099,5036,5038,5053],{"className":5037},[1186],[1099,5039,5041],{"className":5040,"style":1918},[1190],[1099,5042,5044,5047],{"style":5043},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1099,5045],{"className":5046,"style":1199},[1198],[1099,5048,5050],{"className":5049},[1203,1204,1205,1206],[1099,5051,1848],{"className":5052},[1161,1162,1206],[1099,5054,1940],{"className":5055},[1939],[1099,5057,5059],{"className":5058},[1186],[1099,5060,5062],{"className":5061,"style":2305},[1190],[1099,5063],{},[1099,5065,1125],{"className":5066},[1167],[1099,5068,3304],{"className":5069},[1161,1162],[1099,5071,1138],{"className":5072},[1213],[1099,5074],{"className":5075,"style":1614},[1342],[1099,5077,2988],{"className":5078},[1804],[1099,5080],{"className":5081,"style":1614},[1342],[1099,5083,5085,5089,5093,5096,5145,5148,5191,5194,5197,5200,5203,5206],{"className":5084},[1152],[1099,5086],{"className":5087,"style":5088},[1156],"height:1.1858em;vertical-align:-0.4358em;",[1099,5090,4802],{"className":5091,"style":5092},[1161,1162],"margin-right:0.0528em;",[1099,5094],{"className":5095,"style":1343},[1342],[1099,5097,5099,5105],{"className":5098},[1347],[1099,5100,4807],{"className":5101,"style":5104},[1347,5102,5103],"op-symbol","small-op","position:relative;top:0em;",[1099,5106,5108],{"className":5107},[1178],[1099,5109,5111,5136],{"className":5110},[1182,1911],[1099,5112,5114,5133],{"className":5113},[1186],[1099,5115,5118],{"className":5116,"style":5117},[1190],"height:0.162em;",[1099,5119,5121,5124],{"style":5120},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1099,5122],{"className":5123,"style":1199},[1198],[1099,5125,5127],{"className":5126},[1203,1204,1205,1206],[1099,5128,5130],{"className":5129},[1161,1206],[1099,5131,1851],{"className":5132,"style":1934},[1161,1162,1206],[1099,5134,1940],{"className":5135},[1939],[1099,5137,5139],{"className":5138},[1186],[1099,5140,5143],{"className":5141,"style":5142},[1190],"heig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",[1099,5326,5328,5389],{"className":5327},[1102],[1099,5329,5331],{"className":5330},[1106],[1108,5332,5333],{"xmlns":1110},[1112,5334,5335,5386],{},[1115,5336,5337,5347,5349,5351,5353,5355,5357,5359,5361,5363,5365,5367,5369,5371,5373,5375,5377,5384],{},[1839,5338,5339,5341],{},[1118,5340,1095],{},[1115,5342,5343,5345],{},[1118,5344,1848],{},[1118,5346,1851],{},[1122,5348,1125],{"stretchy":1124},[1118,5350,3304],{},[1122,5352,1138],{"stretchy":1124},[1122,5354,1387],{},[1118,5356,3993],{},[1122,5358,1312],{},[1122,5360,1125],{"stretchy":1124},[1122,5362,4004],{},[1118,5364,4007],{},[1118,5366,4665],{},[1122,5368,1138],{"stretchy":1124},[1122,5370,3990],{},[1122,5372,1125],{"stretchy":1124},[1133,5374,1651],{},[1122,5376,4004],{},[1839,5378,5379,5381],{},[1118,5380,1095],{},[2759,5382,5383],{},"loss",[1122,5385,1138],{"stretchy":1124},[1140,5387,5388],{"encoding":1142},"p_{ij}(t) = \\exp(-\\lambda \\tau)\\cdot(1 - p_{\\text{loss}})",[1099,5390,5392,5459,5492,5513],{"className":5391,"ariaHidden":1148},[1147],[1099,5393,5395,5398,5441,5444,5447,5450,5453,5456],{"className":5394},[1152],[1099,5396],{"className":5397,"style":1895},[1156],[1099,5399,5401,5404],{"className":5400},[1161],[1099,5402,1095],{"className":5403},[1161,1162],[1099,5405,5407],{"className":5406},[1178],[1099,5408,5410,5433],{"className":5409},[1182,1911],[1099,5411,5413,5430],{"className":5412},[1186],[1099,5414,5416],{"className":5415,"style":1918},[1190],[1099,5417,5418,5421],{"style":1921},[1099,5419],{"className":5420,"style":1199},[1198],[1099,5422,5424],{"className":5423},[1203,1204,1205,1206],[1099,5425,5427],{"className":5426},[1161,1206],[1099,5428,1935],{"className":5429,"style":1934},[1161,1162,1206],[1099,5431,1940],{"className":5432},[1939],[1099,5434,5436],{"className":5435},[1186],[1099,5437,5439],{"className":5438,"style":1947},[1190],[1099,5440],{},[1099,5442,1125],{"className":5443},[1167],[1099,5445,3304],{"className":5446},[1161,1162],[1099,5448,1138],{"className":5449},[1213],[1099,5451],{"className":5452,"style":1411},[1342],[1099,5454,1387],{"className":5455},[1415],[1099,5457],{"className":5458,"style":1411},[1342],[1099,5460,5462,5465,5468,5471,5474,5477,5480,5483,5486,5489],{"className":5461},[1152],[1099,5463],{"className":5464,"style":1329},[1156],[1099,5466,3993],{"className":5467},[1347],[1099,5469,1125],{"className":5470},[1167],[1099,5472,4004],{"className":5473},[1161],[1099,5475,4007],{"className":5476},[1161,1162],[1099,5478,4665],{"className":5479,"style":4696},[1161,1162],[1099,5481,1138],{"className":5482},[1213],[1099,5484],{"className":5485,"style":1614},[1342],[1099,5487,3990],{"className":5488},[1804],[1099,5490],{"className":5491,"style":1614},[1342],[1099,5493,5495,5498,5501,5504,5507,5510],{"className":5494},[1152],[1099,5496],{"className":5497,"style":1329},[1156],[1099,5499,1125],{"className":5500},[1167],[1099,5502,1651],{"className":5503},[1161],[1099,5505],{"className":5506,"style":1614},[1342],[1099,5508,4004],{"className":5509},[1804],[1099,5511],{"className":5512,"style":1614},[1342],[1099,5514,5516,5519,5565],{"className":5515},[1152],[1099,5517],{"className":5518,"style":1329},[1156],[1099,5520,5522,5525],{"className":5521},[1161],[1099,5523,1095],{"className":5524},[1161,1162],[1099,5526,5528],{"className":5527},[1178],[1099,5529,5531,5557],{"className":5530},[1182,1911],[1099,5532,5534,5554],{"className":5533},[1186],[1099,5535,5537],{"className":5536,"style":3607},[1190],[1099,5538,5539,5542],{"style":1921},[1099,5540],{"className":5541,"style":1199},[1198],[1099,5543,5545],{"className":5544},[1203,1204,1205,1206],[1099,5546,5548],{"className":5547},[1161,1206],[1099,5549,5551],{"className":5550},[1161,2777,1206],[1099,5552,5383],{"className":5553},[1161,1206],[1099,5555,1940],{"className":5556},[1939],[1099,5558,5560],{"className":5559},[1186],[1099,5561,5563],{"className":5562,"style":2305},[1190],[1099,5564],{},[1099,5566,1138],{"className":5567},[1213]," 表征消息有效性随延迟与丢失概率的衰减,从而为异步环境下\"最长链信息以概率方式逐步趋同\"提供统一的数学描述。",[1095,5570,5571,5574,5575,5630,5631,5694],{},[1544,5572,5573],{},"策略层面",",比较对象仍限定为直接邻居的最近状态,以维持 ",[1099,5576,5578,5601],{"className":5577},[1102],[1099,5579,5581],{"className":5580},[1106],[1108,5582,5583],{"xmlns":1110},[1112,5584,5585,5599],{},[1115,5586,5587,5589,5591,5593,5595,5597],{},[1118,5588,1120],{},[1122,5590,1125],{"stretchy":1124},[1118,5592,1309],{},[1122,5594,1312],{},[1118,5596,1131],{},[1122,5598,1138],{"stretchy":1124},[1140,5600,2335],{"encoding":1142},[1099,5602,5604],{"className":5603,"ariaHidden":1148},[1147],[1099,5605,5607,5610,5613,5616,5621,5624,5627],{"className":5606},[1152],[1099,5608],{"className":5609,"style":1329},[1156],[1099,5611,1120],{"className":5612,"style":1163},[1161,1162],[1099,5614,1125],{"className":5615},[1167],[1099,5617,1348,5619],{"className":5618},[1347],[1099,5620,1352],{"style":1351},[1099,5622],{"className":5623,"style":1343},[1342],[1099,5625,1131],{"className":5626,"style":1174},[1161,1162],[1099,5628,1138],{"className":5629},[1213]," 的通信规模;但信息收集与决策方式由确定性周期查询改为时间窗口内的概率性收集与软概率选择:节点以 softmax 形式计算每条候选链成为全局最长链的相对概率,既可确定性地选取概率最高者,亦可按概率随机抽样以增加探索性。在消息成功率较高时,通信复杂度理论上仍保持 ",[1099,5632,5634,5659],{"className":5633},[1102],[1099,5635,5637],{"className":5636},[1106],[1108,5638,5639],{"xmlns":1110},[1112,5640,5641,5657],{},[1115,5642,5643,5645,5647,5649,5651,5653,5655],{},[1118,5644,1120],{},[1122,5646,1125],{"stretchy":1124},[1118,5648,1131],{},[1118,5650,1309],{},[1122,5652,1312],{},[1118,5654,1131],{},[1122,5656,1138],{"stretchy":1124},[1140,5658,1319],{"encoding":1142},[1099,5660,5662],{"className":5661,"ariaHidden":1148},[1147],[1099,5663,5665,5668,5671,5674,5677,5680,5685,5688,5691],{"className":5664},[1152],[1099,5666],{"className":5667,"style":1329},[1156],[1099,5669,1120],{"className":5670,"style":1163},[1161,1162],[1099,5672,1125],{"className":5673},[1167],[1099,5675,1131],{"className":5676,"style":1174},[1161,1162],[1099,5678],{"className":5679,"style":1343},[1342],[1099,5681,1348,5683],{"className":5682},[1347],[1099,5684,1352],{"style":1351},[1099,5686],{"className":5687,"style":1343},[1342],[1099,5689,1131],{"className":5690,"style":1174},[1161,1162],[1099,5692,1138],{"className":5693},[1213],"。",[1095,5696,5697,5700,5701,5750],{},[1544,5698,5699],{},"机制层面",",针对异步网络延迟无界、乱序、丢失的根本难题,设计了自适应时间窗口机制:窗口大小 ",[1099,5702,5704,5726],{"className":5703},[1102],[1099,5705,5707],{"className":5706},[1106],[1108,5708,5709],{"xmlns":1110},[1112,5710,5711,5723],{},[1115,5712,5713,5715,5717,5719,5721],{},[1118,5714,2387],{"mathvariant":2386},[1118,5716,3304],{},[1122,5718,1125],{"stretchy":1124},[1118,5720,3304],{},[1122,5722,1138],{"stretchy":1124},[1140,5724,5725],{"encoding":1142},"\\Delta t(t)",[1099,5727,5729],{"className":5728,"ariaHidden":1148},[1147],[1099,5730,5732,5735,5738,5741,5744,5747],{"className":5731},[1152],[1099,5733],{"className":5734,"style":1329},[1156],[1099,5736,2387],{"className":5737},[1161],[1099,5739,3304],{"className":5740},[1161,1162],[1099,5742,1125],{"className":5743},[1167],[1099,5745,3304],{"className":5746},[1161,1162],[1099,5748,1138],{"className":5749},[1213]," 依当前网络延迟估计(均值加标准差)动态调整,节点在滑动窗口内收集所有到达消息,并利用消息携带的发送时间戳对乱序消息进行逻辑重排序。实验表明,自适应窗口相较固定窗口或无窗口机制,在收敛时间与消息顺序错误率上均有显著改善。",[1095,5752,5753,5756,5757,5809,5810,1629,5982,6043,6044,6121,6122,6174,6175,6233,6234,6293],{},[1544,5754,5755],{},"理论与实验方面",",给出了异步环境下以概率 ",[1099,5758,5760,5778],{"className":5759},[1102],[1099,5761,5763],{"className":5762},[1106],[1108,5764,5765],{"xmlns":1110},[1112,5766,5767,5775],{},[1115,5768,5769,5771,5773],{},[1133,5770,1651],{},[1122,5772,4004],{},[1118,5774,2530],{},[1140,5776,5777],{"encoding":1142},"1-\\delta",[1099,5779,5781,5800],{"className":5780,"ariaHidden":1148},[1147],[1099,5782,5784,5788,5791,5794,5797],{"className":5783},[1152],[1099,5785],{"className":5786,"style":5787},[1156],"height:0.7278em;vertical-align:-0.0833em;",[1099,5789,1651],{"className":5790},[1161],[1099,5792],{"className":5793,"style":1614},[1342],[1099,5795,4004],{"className":5796},[1804],[1099,5798],{"className":5799,"style":1614},[1342],[1099,5801,5803,5806],{"className":5802},[1152],[1099,5804],{"className":5805,"style":1403},[1156],[1099,5807,2530],{"className":5808,"style":2546},[1161,1162]," 收敛的收敛性定理,并提供概率单调性、概率传播性与(概率意义下的)有限性证明思路,收敛时间的概率上界为 ",[1099,5811,5813,5851],{"className":5812},[1102],[1099,5814,5816],{"className":5815},[1106],[1108,5817,5818],{"xmlns":1110},[1112,5819,5820,5848],{},[1115,5821,5822,5824,5826,5828,5830,5838,5841],{},[1118,5823,4280],{},[1122,5825,4283],{},[1118,5827,4286],{},[1122,5829,3990],{},[5831,5832,5833,5835],"mover",{"accent":1148},[1118,5834,4665],{},[1122,5836,5837],{},"ˉ",[1118,5839,5840],{"mathvariant":2386},"\u002F",[1839,5842,5843,5845],{},[1118,5844,1095],{},[2759,5846,5847],{},"success",[1140,5849,5850],{"encoding":1142},"T \\le D \\cdot \\bar{\\tau} \u002F p_{\\text{success}}",[1099,5852,5854,5872,5890],{"className":5853,"ariaHidden":1148},[1147],[1099,5855,5857,5860,5863,5866,5869],{"className":5856},[1152],[1099,5858],{"className":5859,"style":1775},[1156],[1099,5861,4280],{"className":5862,"style":3412},[1161,1162],[1099,5864],{"className":5865,"style":1411},[1342],[1099,5867,4283],{"className":5868},[1415],[1099,5870],{"className":5871,"style":1411},[1342],[1099,5873,5875,5878,5881,5884,5887],{"className":5874},[1152],[1099,5876],{"className":5877,"style":1532},[1156],[1099,5879,4286],{"className":5880,"style":1163},[1161,1162],[1099,5882],{"className":5883,"style":1614},[1342],[1099,5885,3990],{"className":5886},[1804],[1099,5888],{"className":5889,"style":1614},[1342],[1099,5891,5893,5896,5932,5935],{"className":5892},[1152],[1099,5894],{"className":5895,"style":1329},[1156],[1099,5897,5900],{"className":5898},[1161,5899],"accent",[1099,5901,5903],{"className":5902},[1182],[1099,5904,5906],{"className":5905},[1186],[1099,5907,5910,5919],{"className":5908,"style":5909},[1190],"height:0.5678em;",[1099,5911,5913,5916],{"style":5912},"top:-3em;",[1099,5914],{"className":5915,"style":4900},[1198],[1099,5917,4665],{"className":5918,"style":4696},[1161,1162],[1099,5920,5921,5924],{"style":5912},[1099,5922],{"className":5923,"style":4900},[1198],[1099,5925,5929],{"className":5926,"style":5928},[5927],"accent-body","left:-0.2222em;",[1099,5930,5837],{"className":5931},[1161],[1099,5933,5840],{"className":5934},[1161],[1099,5936,5938,5941],{"className":5937},[1161],[1099,5939,1095],{"className":5940},[1161,1162],[1099,5942,5944],{"className":5943},[1178],[1099,5945,5947,5974],{"className":5946},[1182,1911],[1099,5948,5950,5971],{"className":5949},[1186],[1099,5951,5954],{"className":5952,"style":5953},[1190],"height:0.1514em;",[1099,5955,5956,5959],{"style":1921},[1099,5957],{"className":5958,"style":1199},[1198],[1099,5960,5962],{"className":5961},[1203,1204,1205,1206],[1099,5963,5965],{"className":5964},[1161,1206],[1099,5966,5968],{"className":5967},[1161,2777,1206],[1099,5969,5847],{"className":5970},[1161,1206],[1099,5972,1940],{"className":5973},[1939],[1099,5975,5977],{"className":5976},[1186],[1099,5978,5980],{"className":5979,"style":2305},[1190],[1099,5981],{},[1099,5983,5985,6003],{"className":5984},[1102],[1099,5986,5988],{"className":5987},[1106],[1108,5989,5990],{"xmlns":1110},[1112,5991,5992,6000],{},[1115,5993,5994],{},[5831,5995,5996,5998],{"accent":1148},[1118,5997,4665],{},[1122,5999,5837],{},[1140,6001,6002],{"encoding":1142},"\\bar{\\tau}",[1099,6004,6006],{"className":6005,"ariaHidden":1148},[1147],[1099,6007,6009,6012],{"className":6008},[1152],[1099,6010],{"className":6011,"style":5909},[1156],[1099,6013,6015],{"className":6014},[1161,5899],[1099,6016,6018],{"className":6017},[1182],[1099,6019,6021],{"className":6020},[1186],[1099,6022,6024,6032],{"className":6023,"style":5909},[1190],[1099,6025,6026,6029],{"style":5912},[1099,6027],{"className":6028,"style":4900},[1198],[1099,6030,4665],{"className":6031,"style":4696},[1161,1162],[1099,6033,6034,6037],{"style":5912},[1099,6035],{"className":6036,"style":4900},[1198],[1099,6038,6040],{"className":6039,"style":5928},[5927],[1099,6041,5837],{"className":6042},[1161]," 为平均延迟、",[1099,6045,6047,6065],{"className":6046},[1102],[1099,6048,6050],{"className":6049},[1106],[1108,6051,6052],{"xmlns":1110},[1112,6053,6054,6062],{},[1115,6055,6056],{},[1839,6057,6058,6060],{},[1118,6059,1095],{},[2759,6061,5847],{},[1140,6063,6064],{"encoding":1142},"p_{\\text{success}}",[1099,6066,6068],{"className":6067,"ariaHidden":1148},[1147],[1099,6069,6071,6075],{"className":6070},[1152],[1099,6072],{"className":6073,"style":6074},[1156],"height:0.625em;vertical-align:-0.1944em;",[1099,6076,6078,6081],{"className":6077},[1161],[1099,6079,1095],{"className":6080},[1161,1162],[1099,6082,6084],{"className":6083},[1178],[1099,6085,6087,6113],{"className":6086},[1182,1911],[1099,6088,6090,6110],{"className":6089},[1186],[1099,6091,6093],{"className":6092,"style":5953},[1190],[1099,6094,6095,6098],{"style":1921},[1099,6096],{"className":6097,"style":1199},[1198],[1099,6099,6101],{"className":6100},[1203,1204,1205,1206],[1099,6102,6104],{"className":6103},[1161,1206],[1099,6105,6107],{"className":6106},[1161,2777,1206],[1099,6108,5847],{"className":6109},[1161,1206],[1099,6111,1940],{"className":6112},[1939],[1099,6114,6116],{"className":6115},[1186],[1099,6117,6119],{"className":6118,"style":2305},[1190],[1099,6120],{}," 为消息成功率。在 100 节点私有链结合 Sepolia 测试网数据的实验中,相较传统 PoW 与 GHOST,通信开销降低约 90.5%,收敛时间缩短 35% 以上,且在 ",[1099,6123,6125,6144],{"className":6124},[1102],[1099,6126,6128],{"className":6127},[1106],[1108,6129,6130],{"xmlns":1110},[1112,6131,6132,6141],{},[1115,6133,6134,6136,6138],{},[1133,6135,1651],{},[1122,6137,2622],{},[1133,6139,6140],{},"5",[1140,6142,6143],{"encoding":1142},"1\\sim 5",[1099,6145,6147,6165],{"className":6146,"ariaHidden":1148},[1147],[1099,6148,6150,6153,6156,6159,6162],{"className":6149},[1152],[1099,6151],{"className":6152,"style":1425},[1156],[1099,6154,1651],{"className":6155},[1161],[1099,6157],{"className":6158,"style":1411},[1342],[1099,6160,2622],{"className":6161},[1415],[1099,6163],{"className":6164,"style":1411},[1342],[1099,6166,6168,6171],{"className":6167},[1152],[1099,6169],{"className":6170,"style":1425},[1156],[1099,6172,6140],{"className":6173},[1161]," 秒延迟、",[1099,6176,6178,6201],{"className":6177},[1102],[1099,6179,6181],{"className":6180},[1106],[1108,6182,6183],{"xmlns":1110},[1112,6184,6185,6198],{},[1115,6186,6187,6189,6191,6193,6196],{},[1133,6188,6140],{},[1118,6190,2619],{"mathvariant":2386},[1122,6192,2622],{},[1133,6194,6195],{},"20",[1118,6197,2619],{"mathvariant":2386},[1140,6199,6200],{"encoding":1142},"5\\%\\sim 20\\%",[1099,6202,6204,6223],{"className":6203,"ariaHidden":1148},[1147],[1099,6205,6207,6210,6214,6217,6220],{"className":6206},[1152],[1099,6208],{"className":6209,"style":2640},[1156],[1099,6211,6213],{"className":6212},[1161],"5%",[1099,6215],{"className":6216,"style":1411},[1342],[1099,6218,2622],{"className":6219},[1415],[1099,6221],{"className":6222,"style":1411},[1342],[1099,6224,6226,6229],{"className":6225},[1152],[1099,6227],{"className":6228,"style":2640},[1156],[1099,6230,6232],{"className":6231},[1161],"20%"," 丢包率下仍保持 ",[1099,6235,6237,6261],{"className":6236},[1102],[1099,6238,6240],{"className":6239},[1106],[1108,6241,6242],{"xmlns":1110},[1112,6243,6244,6258],{},[1115,6245,6246,6249,6251,6253,6256],{},[1133,6247,6248],{},"92",[1118,6250,2619],{"mathvariant":2386},[1122,6252,2622],{},[1133,6254,6255],{},"98",[1118,6257,2619],{"mathvariant":2386},[1140,6259,6260],{"encoding":1142},"92\\%\\sim 98\\%",[1099,6262,6264,6283],{"className":6263,"ariaHidden":1148},[1147],[1099,6265,6267,6270,6274,6277,6280],{"className":6266},[1152],[1099,6268],{"className":6269,"style":2640},[1156],[1099,6271,6273],{"className":6272},[1161],"92%",[1099,6275],{"className":6276,"style":1411},[1342],[1099,6278,2622],{"className":6279},[1415],[1099,6281],{"className":6282,"style":1411},[1342],[1099,6284,6286,6289],{"className":6285},[1152],[1099,6287],{"className":6288,"style":2640},[1156],[1099,6290,6292],{"className":6291},[1161],"98%"," 的收敛成功率,验证了时间窗口机制对异步网络的关键适配作用。",[1091,6295,6297],{"id":6296},"六结论","六、结论",[1095,6299,6300,6301,6373,6374,1288,6447,6510],{},"本文的工作可归纳为\"数学建模 + 算法设计 + 实验验证\"三项，将网络动力学理论系统应用于最长链共识,建立了基于延迟耦合的连续时间链长度与权重演化模型;在同步网络假设下,将最长链选择策略的比较对象由全局收缩为局部邻居、触发时机由事件驱动改为周期主动询问;提出了基于链权重(含时间衰减项)的快速收敛机制,显著加速分叉解决;给出了同步网络下局部决策策略的收敛性定理与时间上界 ",[1099,6302,6304,6325],{"className":6303},[1102],[1099,6305,6307],{"className":6306},[1106],[1108,6308,6309],{"xmlns":1110},[1112,6310,6311,6323],{},[1115,6312,6313,6315,6317,6319,6321],{},[1118,6314,4280],{},[1122,6316,4283],{},[1118,6318,4286],{},[1122,6320,3990],{},[1118,6322,2387],{"mathvariant":2386},[1140,6324,4293],{"encoding":1142},[1099,6326,6328,6346,6364],{"className":6327,"ariaHidden":1148},[1147],[1099,6329,6331,6334,6337,6340,6343],{"className":6330},[1152],[1099,6332],{"className":6333,"style":1775},[1156],[1099,6335,4280],{"className":6336,"style":3412},[1161,1162],[1099,6338],{"className":6339,"style":1411},[1342],[1099,6341,4283],{"className":6342},[1415],[1099,6344],{"className":6345,"style":1411},[1342],[1099,6347,6349,6352,6355,6358,6361],{"className":6348},[1152],[1099,6350],{"className":6351,"style":1532},[1156],[1099,6353,4286],{"className":6354,"style":1163},[1161,1162],[1099,6356],{"className":6357,"style":1614},[1342],[1099,6359,3990],{"className":6360},[1804],[1099,6362],{"className":6363,"style":1614},[1342],[1099,6365,6367,6370],{"className":6366},[1152],[1099,6368],{"className":6369,"style":1532},[1156],[1099,6371,2387],{"className":6372},[1161],";将通信复杂度由 ",[1099,6375,6377,6400],{"className":6376},[1102],[1099,6378,6380],{"className":6379},[1106],[1108,6381,6382],{"xmlns":1110},[1112,6383,6384,6398],{},[1115,6385,6386,6388,6390,6396],{},[1118,6387,1120],{},[1122,6389,1125],{"stretchy":1124},[1127,6391,6392,6394],{},[1118,6393,1131],{},[1133,6395,1135],{},[1122,6397,1138],{"stretchy":1124},[1140,6399,1143],{"encoding":1142},[1099,6401,6403],{"className":6402,"ariaHidden":1148},[1147],[1099,6404,6406,6409,6412,6415,6444],{"className":6405},[1152],[1099,6407],{"className":6408,"style":1157},[1156],[1099,6410,1120],{"className":6411,"style":1163},[1161,1162],[1099,6413,1125],{"className":6414},[1167],[1099,6416,6418,6421],{"className":6417},[1161],[1099,6419,1131],{"className":6420,"style":1174},[1161,1162],[1099,6422,6424],{"className":6423},[1178],[1099,6425,6427],{"className":6426},[1182],[1099,6428,6430],{"className":6429},[1186],[1099,6431,6433],{"className":6432,"style":1191},[1190],[1099,6434,6435,6438],{"style":1194},[1099,6436],{"className":6437,"style":1199},[1198],[1099,6439,6441],{"className":6440},[1203,1204,1205,1206],[1099,6442,1135],{"className":6443},[1161,1206],[1099,6445,1138],{"className":6446},[1213],[1099,6448,6450,6475],{"className":6449},[1102],[1099,6451,6453],{"className":6452},[1106],[1108,6454,6455],{"xmlns":1110},[1112,6456,6457,6473],{},[1115,6458,6459,6461,6463,6465,6467,6469,6471],{},[1118,6460,1120],{},[1122,6462,1125],{"stretchy":1124},[1118,6464,1131],{},[1118,6466,1309],{},[1122,6468,1312],{},[1118,6470,1131],{},[1122,6472,1138],{"stretchy":1124},[1140,6474,1319],{"encoding":1142},[1099,6476,6478],{"className":6477,"ariaHidden":1148},[1147],[1099,6479,6481,6484,6487,6490,6493,6496,6501,6504,6507],{"className":6480},[1152],[1099,6482],{"className":6483,"style":1329},[1156],[1099,6485,1120],{"className":6486,"style":1163},[1161,1162],[1099,6488,1125],{"className":6489},[1167],[1099,6491,1131],{"className":6492,"style":1174},[1161,1162],[1099,6494],{"className":6495,"style":1343},[1342],[1099,6497,1348,6499],{"className":6498},[1347],[1099,6500,1352],{"style":1351},[1099,6502],{"className":6503,"style":1343},[1342],[1099,6505,1131],{"className":6506,"style":1174},[1161,1162],[1099,6508,1138],{"className":6509},[1213],",并保持最长链规则的基本安全性;最终通过私有链与真实以太坊测试网数据验证了算法在通信效率、收敛速度与链稳定性上的显著优势。",[1095,6512,6513],{},"从整体看,同步版本在较强假设下实现了更优的确定性性能,异步版本则在放宽至真实网络最常见的异步假设后,通过引入概率传播与自适应时间窗口机制,完成了对更困难场景的适应性扩展。二者相辅相成,共同构成一套面向不同网络条件的低复杂度最长链共识方案。",{"title":6515,"searchDepth":6516,"depth":6516,"links":6517},"",4,[6518,6520,6521,6522,6529,6535,6536],{"id":1093,"depth":6519,"text":1093},2,{"id":1365,"depth":6519,"text":1366},{"id":1539,"depth":6519,"text":1540},{"id":2667,"depth":6519,"text":2668,"children":6523},[6524,6526,6527,6528],{"id":2672,"depth":6525,"text":2673},3,{"id":2725,"depth":6525,"text":2726},{"id":2955,"depth":6525,"text":2956},{"id":3061,"depth":6525,"text":3062},{"id":3272,"depth":6519,"text":3273,"children":6530},[6531,6532,6533,6534],{"id":3276,"depth":6525,"text":3277},{"id":3460,"depth":6525,"text":3461},{"id":3475,"depth":6525,"text":3476},{"id":4258,"depth":6525,"text":4259},{"id":4545,"depth":6519,"text":4546},{"id":6296,"depth":6519,"text":6297},"md",true,{"uuid":6540,"password":6541,"abstract":6542,"message":6542,"wrong_pass_message":6543,"slots":6544},"ba86f650-f283-11f0-986a-871b27513b0a","zhongye","联系站长以查看密码","如果是项目组成员，请联系站长。WXID:Zhong_ye1",{},15,{"title":1085,"description":6515},"posts\u002F2026\u002F2026-01-16-关于低复杂度最长链共识算法设计",[241,242,243,244],"ldTDmpUNZeC16wvAXpI-Mt9YzKIJQ0gZ__g05VspFDM",1790443286481]