Melgratti, Hernán and Mezzina, Claudio Antares and Ulidowski, Irek - Reversing Place Transition Nets

lmcs:5831 - Logical Methods in Computer Science, October 16, 2020, Volume 16, Issue 4
Reversing Place Transition Nets

Authors: Melgratti, Hernán and Mezzina, Claudio Antares and Ulidowski, Irek

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, for example an occurrence net, can be straightforwardly reversed by adding a reverse transition for each of its forward transitions. Secondly, given a P/T net the standard unfolding construction associates with it 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.

Volume: Volume 16, Issue 4
Published on: October 16, 2020
Submitted on: October 11, 2019
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory


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