Reversibility and Models for Concurrency

There is a growing interest in models of reversible computation driven by exciting application areas such as bio-systems and quantum computing. Reversible process algebras RCCS [Danos, V. and J. Krivine, Reversible communicating systems, in: P. Gardner and N. Yoshida, editors, Proceedings of the 15th International Conference on Concurrency Theory CONCUR 2004, LNCS 3170 (2004), pp. 292–307] and CCSK [Phillips, I.C.C. and I. Ulidowski, Reversing algebraic process calculi, in: Proceedings of 9th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2006, LNCS 3921 (2006), pp. 246–260. Extended version accepted by Journal of Logic and Algebraic Programming] were developed and general techniques for reversing other process operators were proposed. The paper shows that the notion of reversibility can bridge the gap between some interleaving models and non-interleaving models of concurrency, and makes them interchangeable. We prove that transition systems associated with reversible process algebras are equivalent as models to labelled prime event structures. Furthermore, we show that forward-reverse bisimulation corresponds to hereditary history-preserving bisimulation in the setting with no auto-concurrency and no auto-causation.