通过自动机理论经济设计解决CAP问题：面向实时分区容忍系统的统一数学框架
Resolving CAP Through Automata-Theoretic Economic Design: A Unified Mathematical Framework for Real-Time Partition-Tolerant Systems
AI总结：
本文提出一个融合自动机理论与经济激励的统一数学框架，将CAP权衡建模为约束优化问题，通过博弈论机制证明在有界ε裕度内可同时保持可用性与一致性，从而扩展经典CAP限制。
摘要：
CAP定理断言一致性、可用性与分区容忍性之间存在三元悖论。本文引入一个严格的基于自动机理论并具有经济学基础的框架，将CAP权衡重新表述为约束优化问题。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对抗性分区网络中稳定共识行为。通过将博弈论机制纳入全局转移语义，我们定义了关于收敛性、活性与正确性的可证明界限。我们的结果表明，在有界的ε裕度内可以同时保持可用性与一致性，从而通过形式化经济控制有效扩展了经典CAP限制。
英文摘要：
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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