Bridging Causal Reversibility and Time Reversibility: A Stochastic Process Algebraic Approach

TL;DR

This paper unifies causal and time reversibility in stochastic systems using a process algebra approach, enabling systems to be reversible in both causality and stochastic behavior.

Contribution

It introduces a stochastic process calculus that ensures both causal and time reversibility, bridging two distinct theories of reversibility in concurrent systems.

Findings

Conditions for causal and time reversibility are identified.

A stochastic bisimilarity is developed for forward and backward analysis.

The approach facilitates reversible stochastic system design and analysis.

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.