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.

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

“…To demonstrate the practicality of our algorithm, we present a few case studies including a protocol that ensures reaching agreement in uni-rings when processes of the ring disagree on a value, and a parity protocol that guarantees a common parity amongst the processes. We conjecture that the implementation of our algorithm will provide a highly efficient synthesis tool as our previous work [18] on the synthesis of fault-tolerant parameterized uni-rings confirms our belief. Organization.…”

“…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.…”

“…The closest work to this paper includes our previous work on the synthesis of self-stabilizing parameterized uni-rings [18], where a protocol is expected to recover to a set of states from any state. In the synthesis of self-stabilization, R = true and Q captures a set of legitimate states to which recovery is required.…”