Safety Analysis of Parameterised Networks with Non-Blocking Rendez-Vous

TL;DR

This paper analyzes the safety properties of parameterised process networks with non-blocking rendez-vous communication, establishing complexity results and decidability boundaries for coverability and reachability problems.

Contribution

It introduces the non-blocking rendez-vous semantics and provides complexity classifications and decidability results for safety verification in parameterised networks.

Findings

The coverability problem is EXPSPACE-complete.

Polynomial-time solutions exist for protocols with two state partitions.

Reachability of a final state is undecidable under non-blocking semantics.

Abstract

We consider networks of processes that all execute the same finite-state protocol and communicate via a rendez-vous mechanism. When a process requests a rendez-vous, another process can respond to it and they both change their control states accordingly. We focus here on a specific semantics, called non-blocking, where the process requesting a rendez-vous can change its state even if no process can respond to it. In this context, we study the parameterised coverability problem of a configuration, which consists in determining whether there is an initialnumber of processes and an execution allowing to reach a configuration bigger than a given one. We show that this problem is EXPSPACE-complete and can be solved in polynomial time if the protocol is partitioned into two sets of states, the states from which a process can request a rendez-vous and the ones from which it can answer one. We also prove that the problem of the existence of an execution bringing all the processes in a final state is undecidable in our context. These two problems can be solved in polynomial time with the classical rendez-vous semantics.