Affiliations: [a] Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain. defrutos@sip.ucm.es | [b] School of Computing, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. maciej.koutny@ncl.ac.uk | [c] Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland. lukasz.mikulski@mat.umk.pl
Correspondence:
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Address for correspondence: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland. Also affiliated at: Institute of Computer Science, Polish Academy of Sciences, Jana Kazimierza 5, 01-248 Warsaw, Poland
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.
Keywords: Petri net, reversible computation, step semantics, action splitting, net synthesis, direct reversibility, mixed reversibility, weighted activator arcs
