🤖 AI Summary
The CAP theorem imposes a fundamental trade-off among consistency, availability, and partition tolerance in distributed systems, rendering simultaneous strong guarantees impossible. Method: This paper proposes a novel formal framework integrating automata theory with economic incentive mechanisms. It introduces game-theoretic reasoning and economic regulation into state-machine models for the first time, enabling partition-aware modeling and formalizing CAP trade-offs as constrained optimization problems via incentive-augmented global transition semantics. Contribution/Results: The framework transcends classical CAP limitations by guaranteeing both strong consistency and high availability within a bounded error margin ε. Experimental evaluation demonstrates that the system maintains convergence, liveness, and correctness under adversarial network partitions. By unifying formal verification with incentive-aligned design, this work establishes a theoretically rigorous and practically deployable foundation for next-generation distributed consensus protocols.
📝 Abstract
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.