On the k-synchronizability of systems

TL;DR

This paper investigates k-synchronizability in systems, proving that both reachability and membership problems are decidable for mailbox and peer-to-peer automata, correcting previous proof issues.

Contribution

It establishes decidability results for reachability and membership problems in k-synchronizable systems, improving upon prior work with corrected proofs.

Findings

Reachability is decidable for k-synchronizable systems.

Membership problem for k-synchronizability is decidable.

Proofs address and fix issues in earlier attempts.

Abstract

In this paper, we work on the notion of k-synchronizability: a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be divided into a succession of k-bounded interaction phases. We show two results (both for mailbox and peer-to-peer automata): first, the reachability problem is decidable for k-synchronizable systems; second, the membership problem (whether a given system is k-synchronizable) is decidable as well. Our proofs fix several important issues in previous attempts to prove these two results for mailbox automata.