A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes

TL;DR

This paper introduces Constrained Petri Nets and a logic called CML for modeling and reasoning about unbounded dynamic networks of infinite-state processes, enabling various verification tasks.

Contribution

It presents a generic framework with decidability results for a logic over infinite-state process networks, extending Petri nets with data constraints.

Findings

Decidability of CML satisfiability for certain fragments.

Closure of the logic under post and pre image computations.

Application to invariance, pre-post reasoning, and bounded reachability.

Abstract

We propose a framework for reasoning about unbounded dynamic networks of infinite-state processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a first-order logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens. We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, pre-post condition reasoning, and bounded reachability analysis.