Towards Bridging Time and Causal Reversibility

Abstract

Causal consistent reversibility blends causality and reversibility. For a concurrent system, it says that an action can be undone provided this has no consequences, thereby making it possible to bring the system back to a past consistent state. Time reversibility is considered instead in the performance evaluation field. A continuous-time Markov chain is time reversible if its behavior remains the same when the direction of time is reversed. We try to bridge these two theories by showing the conditions under which both causal consistent reversibility and time reversibility can be achieved in the setting of a stochastic process algebra.

The Reversible Temporal Process Language

“…A deep comparison between deterministic time, used by TPL, and stochastic time used by stochastic process algebras can be found in [1]. Further investigation on the relation between our work and [2], studying reversibility in Markov chains, is left for future work. The treatment of passage of time shares some similarities with broadcast [24]: time actions affect parallel components in the same way, and idempatience can be seen as unavailability of top-level receivers.…”

“…By exploiting causality information, causalconsistent reversible debuggers allow one to undo just the steps which led (are causally related) to a misbehaviour, reducing the number of steps/spurious causes and helping to understand its root cause. In the last years several reversible semantics for concurrency have been developed, see, e.g., [8,7,18,2,22]. However, none of them takes into account time 1 .…”

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

“…We finally show that reversibility is causally consistent in our concurrent framework. This can be done in two ways: either by adapting the original proof of [8], as we did in [5], or by using the general technique provided by [30]. We opt for the latter, according to which causal consistency stems from the diamond property, backward transition independencewhich generalizes the concept of backward determinism used for reversible sequential languages [47] -and past well foundedness -which ensures that reachable processes have a finite past.…”

“…This paper, which is a revised and enriched version of [5], is organized as follows. In Sections 2 and 3 we recall background information about causal consistent reversibility and time reversibility, respectively.…”

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

“…This paper, which is a revised and enriched version of [BM20], is organized as follows. In Sections 2 and 3 we recall background notions about causal reversibility and time reversibility, respectively.…”