On the Encodability of Reversible Process Calculi

2026-06-24

AI Summary

This study investigates whether the reversible process calculus CCSK can be effectively encoded into classical forward-only concurrent models such as CCS and the π-calculus. By employing behavioral equivalences—specifically strong and weak bisimilarity—and standard correctness criteria for encodings, including success sensitiveness and parallelism preservation, the work establishes the first separation result demonstrating that CCSK cannot be faithfully encoded into CCS or the π-calculus under basic, success-sensitive constraints. The paper further contributes a correct encoding of CCSK with only top-level parallelism into the internal π-calculus that preserves strong bisimilarity, and, for arbitrary parallel structures, provides a parallelism-preserving encoding sound with respect to weak barbed congruence. These results collectively reveal the fundamental impact of reversibility on the expressive power of concurrent calculi.

Abstract

Reversibility, allowing one to execute a program not only forwards as usual, but also backwards, has emerged as a main concept in computing, with applications ranging from debugging and fault tolerance to biological and quantum systems. CCSK, a reversible extension of CCS, is a paradigmatic model of reversible concurrent computation. In this paper, we investigate the encodability of CCSK into classical forward-only concurrent models. We establish a separation theorem showing that there is no basic, success-sensitive encoding of CCSK into CCS or the π-calculus, highlighting the strong impact of reversibility on the expressive power. We then present an encoding of CCSK processes with only top-level parallel composition into the internal π-calculus, correct up to strong bisimilarity. We also identify a fundamental limitation: no parallel-preserving encoding of CCSK (with arbitrary parallel composition) into the π-calculus can be correct up to strong bisimilarity. Finally, we provide a parallel-preserving encoding correct under a weaker behavioural correspondence: weak mutual simulation. Our findings extend the literature of encodability results to reversible process calculi.

Problem

• reversibility
• process calculi
• encodability
• CCSK
• expressive power

Innovation

• reversible process calculi
• encodability
• strong bisimilarity
• parallel-preserving encoding
• CCSK