Modal Logic Characterizations of Forward, Reverse, and Forward-Reverse Bisimilarities

TL;DR

This paper provides logical characterizations of forward, reverse, and combined bisimilarities in reversible systems, linking them to trace and branching bisimilarities through modal logic.

Contribution

It introduces modal logic characterizations for various bisimilarities in reversible systems, connecting them to existing equivalences like trace and branching bisimilarity.

Findings

Strong and weak reverse bisimilarities correspond to trace equivalences.

Weak forward-reverse bisimilarity inherits characterizations from branching bisimilarity.

Logical frameworks clarify relationships among different bisimilarities.

Abstract

Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and weak variants of forward-reverse bisimilarity as well as of its two components, i.e., forward bisimilarity and reverse bisimilarity, have been investigated on a minimal process calculus for nondeterministic reversible systems that are sequential, so as to be neutral with respect to interleaving vs. truly concurrent semantics of parallel composition. In this paper we provide logical characterizations for the considered bisimilarities based on forward and backward modalities, which reveals that strong and weak reverse bisimilarities respectively correspond to strong and weak reverse trace equivalences. Moreover, we establish a clear connection between weak forward-reverse bisimilarity and branching bisimilarity, so that the former inherits two further logical characterizations from the latter over a specific class of processes.