On the Reversibility of Live Equal-Conflict Petri Nets
A Petri net is reversible if its initial marking is a home marking, a marking reachable from any reachable marking. This property is fundamental in man-made systems as it lets a system return to its initial state using only internal operations.
Necessary and sufficient conditions are already known for the reversibility of well-formed Choice-Free and ordinary Free-Choice nets. Like the homogeneous Join-Free nets, these nets constitute subclasses of Equal-Conflict nets. In this larger class, the reversibility property is not well understood.
This paper provides the first characterization of reversibility for all the live Equal-Conflict systems by extending, in a weaker form, a known condition that applies to the Choice-Free and Free-Choice subclasses. We also show that this condition is tightly related to the Equal-Conflict class and does not apply to several other classes.
KeywordsReversibility Home markings Liveness Weighted petri nets Characterization Equal-conflict Join-free Choice-free Free-choice
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- 4.de Frutos Escrig, D., Johnen, C.: Decidability of Home Space Property. Tech. Rep. LRI-503, Univ. de Paris-Sud, Centre d’Orsay, LRI (1989)Google Scholar
- 9.López-Grao, J.-P., Colom, J.-M.: Structural Methods for the Control of Discrete Event Dynamic Systems – The Case of the Resource Allocation Problem. In: Seatzu, C., Silva Suárez, M., van Schuppen, J.H. (eds.) Control of Discrete-event Systems. LNCIS, vol. 433, pp. 257–278. Springer, Heidelberg (2013) CrossRefGoogle Scholar
- 13.Sifakis, J.: Structural properties of petri nets. In: Winkowski, J. (ed.) Mathematical Foundations of Computer Science. LNCS, vol. 64, pp. 474–483. Springer, Heidelberg (1978)Google Scholar