Parameterized Verification of Systems with Precise (0,1)-Counter Abstraction

TL;DR

This paper presents a unified framework for verifying parameterized systems with a finite 01-counter abstraction, enabling decidability of key verification problems for various well-structured infinite-state systems.

Contribution

It introduces a new well-structured system class for parameterized verification, unifying and extending previous results for systems like broadcast networks and shared-variable systems.

Findings

Decidable control-state reachability and coverability in the proposed framework

Applicable to a broad class of systems from the literature

Provides simplified and unified verification approach

Abstract

We introduce a new framework for verifying systems with a parametric number of concurrently running processes. The systems we consider are well-structured with respect to a specific well-quasi order. This allows us to decide a wide range of verification problems, including control-state reachability, coverability, and target, in a fixed finite abstraction of the infinite state-space, called a 01-counter system. We show that several systems from the parameterized verification literature fall into this class, including reconfigurable broadcast networks (or systems with lossy broadcast), disjunctive systems, synchronizations and systems with a fixed number of shared finite-domain variables. Our framework provides a simple and unified explanation for the properties of these systems, which have so far been investigated separately. Additionally, it extends and improves on a range of the existing results, and gives rise to other systems with similar properties.