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Investigating Reversibility of Steps in Petri Nets

de Frutos Escrig David, Koutny Maciej, Mikulski Łukasz

Fundamenta Informaticae

2021

Vol. 183, nr 1-2

67--96

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.

Synthesis of Elementary Net Systems with Context Arcs and Localities

Koutny M., Pietkiewicz-Koutny M.

Fundamenta Informaticae

2008

Vol. 88, nr 3

307-328

We investigate the synthesis problem for ENCL-systems, defined as Elementary Net Systems extended with context (inhibitor and activator) arcs and explicit event localities. Since colocated events are meant to be executed synchronously, the behaviour of such systems is captured by step transition systems, where arcs are labelled by sets of events rather than by single events. We completely characterise transition systems generated by ENCL-systems after extending the standard notion of a region - defined as a certain set of states - with explicit information about events which, in particular, are responsible for crossing its border. As a result, we are able to construct, for each such transition system, a suitable ENCL-system generating it.