Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties
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This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties R Q on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constant-space processes under no fairness and interleaving semantics, where R and Q are global state predicates. First, we show that verifying R Q for parameterized protocols on symmetric uni-rings is undecidable, even for deterministic and constant-space processes, and conjunctive state predicates. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy R Q is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we devise a sound and complete polynomial-time algorithm that takes the predicates R and Q, and automatically generates a parameterized protocol that satisfies R Q for unbounded (but finite) ring sizes. Moreover, we present some decidability results for cases where leadsto is required from multiple distinct R predicates to different Q predicates. To demonstrate the practicality of our synthesis method, we synthesize some parameterized protocols, including agreement and parity protocols.
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