Bridging Causal Reversibility and Time Reversibility: A Stochastic Process Algebraic Approach
Marco Bernardo, Claudio A. Mezzina
TL;DR
This work addresses bridging causal reversibility and time reversibility in stochastic concurrent systems by introducing RMPC, a rate-labeled reversible stochastic process calculus. It provides forward and backward operational semantics with action keys that record past synchronization, enabling causal reversibility by construction and enabling conditions that guarantee time reversibility. Time reversibility is shown to hold when backward rates match forward rates or when the syntax restricts parallel composition within action prefixes or choices, enabling efficient analysis and potential product-form steady-state results. The paper also develops Markovian bisimilarity variants for reversible systems and demonstrates their alignment with state-based MB, supporting compositional reasoning and practical reasoning about both functional and performance properties.
Abstract
Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a past consistent state. Time reversibility is instead considered in the field of stochastic processes, mostly for efficient analysis purposes. A performance model based on a continuous-time Markov chain is time reversible if its stochastic behavior remains the same when the direction of time is reversed. We bridge these two theories of reversibility by showing the conditions under which causal reversibility and time reversibility are both ensured by construction. This is done in the setting of a stochastic process calculus, which is then equipped with a variant of stochastic bisimilarity accounting for both forward and backward directions.