Reversible Computation in Cyclic Petri Nets

Petri nets are a mathematical language for modeling and reasoning about distributed systems. In this paper we propose an approach to Petri nets for embedding reversibility, i.e., the ability of reversing an executed sequence of operations at any point during operation. 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 variation of cyclic Petri nets where tokens are persistent and are distinguished from each other by an identity. 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 behavior.