Synthesizing Parameterized Self-stabilizing Rings with Constant-Space Processes

Abstract

This paper investigates the problem of synthesizing parameterized rings that are "self-stabilizing by construction". While it is known that the verification of self-stabilization for parameterized unidirectional rings is undecidable, we present a counterintuitive result that synthesizing such systems is decidable! This is surprising because it is known that, in general, the synthesis of distributed systems is harder than their verification. We also show that synthesizing self-stabilizing bidirectional rings is an undecidable problem. To prove the decidability of synthesis for unidirectional rings, we propose a sound and complete algorithm that performs the synthesis in the local state space of processes. We also generate strongly stabilizing rings where no fairness assumption is made. This is particularly noteworthy because most existing verification and synthesis methods for parameterized systems assume a fair scheduler.

Synthesis of Distributed Agreement-Based Systems with Efficiently-Decidable Verification

“…A similar idea, but based on the notion of well-structured transition systems, is used for the automatic repair of parameterized systems in [21]. The approach in [22] targets parameterized synthesis for self-stabilizing rings, and shows that the problem is decidable even when the corresponding parameterized verification problem is not. The designer provides a set of legitimate states and the size of the template process, and the procedure yields a completed self-stabilizing template.…”

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

“…Theorem 2.15. Synthesizing silent-stabilization for a parameterized uni-ring protocol (with self-disabling, deterministic and constant-space processes) is decidable [42,18]. Theorem 2.16.…”