Reversible computation in nets with bonds

Abstract Reversible computation is a form of computing that allows operations to be executed in both the forward as well as the backward direction. In this paper we propose an approach inspired by Petri nets for the modelling of reversible behaviour. Specifically, we introduce machinery and associated semantics to support the three main forms of reversibility namely, backtracking, causal reversing, and out-of-causal-order reversing in a type of nets where tokens are persistent, distinguished from each other by an identity, and can be connected to each other with the use of bonds. Our formalism is influenced by applications in biochemistry but the methodology can be applied to a wide range of problems that feature reversibility. In particular, we demonstrate the applicability of our approach with a model of the ERK signalling pathway, an example that inherently features reversible behaviour.