Topology-specific synthesis of self-stabilizing parameterized systems with constant-space processes

Abstract

This paper investigates the problem of synthesizing parameterized systems that are self-stabilizing by construction. To this end, we present several significant results. First, we show a counterintuitive result that despite the undecidability of verifying self-stabilization for parameterized unidirectional rings, synthesizing self-stabilizing unidirectional rings is decidable! This is surprising because it is known that, in general, the synthesis of distributed systems is harder than their verification. Second, we present a topology-specific synthesis method (derived from our proof of decidability) that generates the state transition system of template processes of parameterized self-stabilizing systems with elementary unidirectional topologies (e.g., rings, chains, trees). We also provide a software tool that implements our synthesis algorithms and generates interesting self-stabilizing parameterized unidirectional rings in less than 50 microseconds on a regular laptop. We validate the proposed synthesis algorithms for decidable cases in the context of several interesting distributed protocols. Third, we show that synthesis of self-stabilizing bidirectional rings remains undecidable.