Deciding the existence of cut-off in parameterized rendez-vous networks

TL;DR

This paper investigates the existence of a cut-off size in parameterized rendez-vous networks, providing decidability and complexity results for various network configurations and communication assumptions.

Contribution

It introduces the first comprehensive analysis of cut-off existence in parameterized rendez-vous networks, covering different communication and leadership scenarios.

Findings

Decidability results for cut-off existence under various assumptions

Complexity classifications for the problem

Conditions where cut-off determination is feasible or undecidable

Abstract

We study networks of processes which all execute the same finite-state protocol and communicate thanks to a rendez-vous mechanism. Given a protocol, we are interested in checking whether there exists a number, called a cut-off, such that in any networks with a bigger number of participants, there is an execution where all the entities end in some final states. We provide decidability and complexity results of this problem under various assumptions, such as absence/presence of a leader or symmetric/asymmetric rendez-vous.