Automatic Repair and Deadlock Detection for Parameterized Systems

TL;DR

This paper introduces an algorithm for repairing parameterized systems to ensure safety properties and deadlock freedom, utilizing model checking and constraints, with applications to various system types.

Contribution

It presents a novel algorithm combining model checking and constraint solving for system repair and deadlock detection in parameterized systems, including decidability results.

Findings

Algorithm effectively repairs systems to satisfy safety properties.

Deadlock detection is decidable in EXPTIME for disjunctive systems.

Deadlock detection is undecidable for broadcast protocols.

Abstract

We present an algorithm for the repair of parameterized systems. The repair problem is, for a given process implementation, to find a refinement such that a given safety property is satisfied by the resulting parameterized system, and deadlocks are avoided. Our algorithm uses a parameterized model checker to determine the correctness of candidate solutions and employs a constraint system to rule out candidates. We apply this algorithm on systems that can be represented as well-structured transition systems (WSTS), including disjunctive systems, pairwise rendezvous systems, and broadcast protocols. Moreover, we show that parameterized deadlock detection can be decided in EXPTIME for disjunctive systems, and that deadlock detection is in general undecidable for broadcast protocols.