Reversing P/T nets

Abstract

Petri Nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop such semantics for Place/Transitions Petri Nets (P/T nets) based on two observations. Firstly, a net that explicitly expresses causality and conflict among events, e.g., an occurrence net, can be straightforwardly reversed by adding reversal for each of its transitions. Secondly, the standard unfolding construction associates a P/T net with an occurrence net that preserves all of its computation. Consequently, the reversible semantics of a P/T net can be obtained as the reversible semantics of its unfolding. We show that such reversible behaviour can be expressed as a finite net whose tokens are coloured by causal histories. Colours in our encoding resemble the causal memories that are typical in reversible process calculi.