Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties $R \leadsto Q$ 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 $R \leadsto Q$ 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 $R \leadsto Q$ 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 $R \leadsto Q$ 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

Local reasoning for global convergence of parameterized rings

This paper presents a method that can generate Self-Stabilizing (SS) parameterized protocols that are generalizable; i.e., correct for arbitrary number of finite-state processes. Specifically, we present necessary and sufficient conditions specified in the local state space of the representative process of parameterized rings for deadlock-freedom in their global state space. Moreover, we introduce sufficient conditions that guarantee livelock-freedom in arbitrary-sized unidirectional rings. We illustrate the proposed approach in the context of several classic examples including a maximal matching protocol and an agreement protocol. More importantly, the proposed method lays the foundation of an approach for automated design of global convergence in the local state space of the representative process. © 2012 IEEE