Investigating Reversibility of Steps in Petri Nets

TL;DR

This paper explores the reversibility of groups of actions in Petri nets, revealing complexities and proposing solutions for reversing steps rather than individual actions.

Contribution

It introduces the concept of reversing steps in Petri nets, generalizing from single actions, and analyzes the challenges and solutions for this more complex scenario.

Findings

Reversibility of steps is more complex than single actions.

Reversing multisets differs significantly from reversing sets.

Combining split reverses with weighted read arcs offers a viable solution.

Abstract

In reversible computations one is interested in the development of mechanisms allowing to undo the effects of executed actions. The past research has been concerned mainly with reversing single actions. In this paper, we consider the problem of reversing the effect of the execution of groups of actions (steps). Using Petri nets as a system model, we introduce concepts related to this new scenario, generalising notions used in the single action case. We then present properties arising when reverse actions are allowed in place/transition nets (pt-nets). We obtain both positive and negative results, showing that allowing steps makes reversibility more problematic than in the interleaving/sequential case. In particular, we demonstrate that there is a crucial difference between reversing steps which are sets and those which are true multisets. Moreover, in contrast to sequential semantics, splitting reverses does not lead to a general method for reversing bounded pt-nets. We then show that a suitable solution can be obtained by combining split reverses with weighted read arcs.