用数学和经济机制突破分布式系统的CAP极限，让系统在断网时仍能兼顾一致性和可用性。
Resolving CAP Through Automata-Theoretic Economic Design: A Unified Mathematical Framework for Real-Time Partition-Tolerant Systems
- 将系统建模为带分区感知的状态机，引入经济激励机制稳定共识
- 证明在有限误差范围内可同时保证一致性与可用性，突破经典CAP限制
- 适合研究分布式系统设计、区块链共识机制的开发者和研究人员
CAP定理指出一致性、可用性和分区容错性三者不可兼得。本文提出一个基于自动机理论和经济激励的严谨框架，将CAP权衡重构为约束优化问题。我们将分布式系统建模为分区感知的状态机，并嵌入经济激励层以在恶意分片网络中稳定共识行为。通过将博弈论机制融入全局状态转移语义，我们建立了收敛性、活性和正确性的可证明边界。结果表明，在有限ε误差范围内，一致性与可用性可同时保持，通过形式化经济控制有效拓展了经典CAP的界限。
原文摘要 · Abstract (English)
The CAP theorem asserts a trilemma between consistency, availability, and partition tolerance. This paper introduces a rigorous automata-theoretic and economically grounded framework that reframes the CAP trade-off as a constraint optimization problem. We model distributed systems as partition-aware state machines and embed economic incentive layers to stabilize consensus behavior across adversarially partitioned networks. By incorporating game-theoretic mechanisms into the global transition semantics, we define provable bounds on convergence, liveness, and correctness. Our results demonstrate that availability and consistency can be simultaneously preserved within bounded epsilon margins, effectively extending the classical CAP limits through formal economic control.
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