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 live lock-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.