Model-Checking Process Equivalences

TL;DR

This paper introduces a logical framework using modal fixpoint logic to define and verify various process equivalences, enabling model checking techniques to be applied for process comparison.

Contribution

It presents a unified logical approach to characterize many process equivalences and demonstrates how to perform model checking for these using symbolic and partial evaluation methods.

Findings

Framework captures many process equivalences with fixed formulas.

Model checking can be applied to verify process equivalences.

Partial evaluation yields decision procedures for process equivalences.

Abstract

Process equivalences are formal methods that relate programs and system which, informally, behave in the same way. Since there is no unique notion of what it means for two dynamic systems to display the same behaviour there are a multitude of formal process equivalences, ranging from bisimulation to trace equivalence, categorised in the linear-time branching-time spectrum. We present a logical framework based on an expressive modal fixpoint logic which is capable of defining many process equivalence relations: for each such equivalence there is a fixed formula which is satisfied by a pair of processes if and only if they are equivalent with respect to this relation. We explain how to do model checking, even symbolically, for a significant fragment of this logic that captures many process equivalences. This allows model checking technology to be used for process equivalence checking. We show how partial evaluation can be used to obtain decision procedures for process equivalences from the generic model checking scheme.