Parameterized safety verification of round-based shared-memory systems

TL;DR

This paper addresses the challenge of verifying safety in round-based shared-memory distributed algorithms with unbounded processes and registers, proving PSPACE-completeness and providing bounds on error executions.

Contribution

It introduces a parameterized verification approach for such algorithms, establishing complexity results and bounds on error states.

Findings

Safety verification is PSPACE-complete.

Exponential bounds on minimal processes for errors.

Bounds on rounds where errors can occur.

Abstract

We consider the parameterized verification problem for distributed algorithms where the goal is to develop techniques to prove the correctness of a given algorithm regardless of the number of participating processes. Motivated by an asynchronous binary consensus algorithm [J. Aspnes, Fast deterministic consensus in a noisy environment. Journal of Algorithms, 2002], we consider round-based distributed algorithms communicating with shared memory. A particular challenge in these systems is that 1) the number of processes is unbounded, and, more importantly, 2) there is a fresh set of registers at each round. A~verification algorithm thus needs to manage both sources of infinity. In this setting, we prove that the safety verification problem, which consists in deciding whether all possible executions avoid a given error state, is PSPACE-complete. For~negative instances of the safety verification problem, we~also provide exponential lower and upper bounds on the minimal number of processes needed for an error execution and on the minimal round on which the error state can be covered.