Claudio Antares Mezzina

Ivan Lanese, Claudio Antares Mezzina, Iain Phillips et al.

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.

Hernán Melgratti, Claudio Antares Mezzina, G. Michele Pinna

Event structures have emerged as a foundational model for concurrent computation, explaining computational processes by outlining the events and the relationships that dictate their execution. They play a pivotal role in the study of key aspects of concurrent computation models, such as causality and independence, and have found applications across a broad range of languages and models, spanning realms like persistence, probabilities, and quantum computing. Recently, event structures have been extended to address reversibility, where computational processes can undo previous computations. In this context, reversible event structures provide abstract representations of processes capable of both forward and backward steps in a computation. Since their introduction, event structures have played a crucial role in bridging operational models, traditionally exemplified by Petri nets and process calculi, with denotational ones, i.e., algebraic domains. In this context, we revisit the standard connection between Petri nets and event structures under the lenses of reversibility. Specifically, we introduce a subset of contextual Petri nets, dubbed reversible causal nets, that precisely correspond to reversible prime event structures. The distinctive feature of reversible causal nets lies in deriving causality from inhibitor arcs, departing from the conventional dependence on the overlap between the post and preset of transitions. In this way, we are able to operationally explain the full model of reversible prime event structures.