Verification and Synthesis of Responsive Symmetric Uni-Rings

Document Type

Article

Publication Date

11-2022

Department

Department of Computer Science

Abstract

This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic, self-disabling and constant-space processes. First, we show that when R and Q are conjunctive global state predicates, verifying ‘R leadsto Q’ (denoted Rˆ Q) for parameterized protocols on symmetric unirings is undecidable. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy Rˆ Q is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we design and implement a sound and complete algorithm that takes the predicates R and Q, and automatically generates a parameterized protocol that satisfies Rˆ Q for unbounded (but finite) ring sizes. Moreover, we show that verifying leadsto properties remains undecidable even if R and Q are local state predicates! This result would lead to the impossibility of computing a cutoff for local leadsto on symmetric rings of deterministic, self-disabling and constant-space processes. We further show that verifying local and global deadlocks in our formal setting are decidable problems. We also present a cutoff theorem that enables the construction of symmetric rings where deadlocks are reachable.

Publication Title

IEEE TRANSACTIONS ON SOFTWARE ENGINEERING

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