Reversible computations constitute an unconventional form of computing where any sequence of performed operations can be undone by executing in reverse order at any point during a computation. It has been attracting increasing attention as it provides opportunities for low-power computation, being at the same time essential or eligible in various applications. In recent work, we have proposed a structural way of translating Reversing Petri Nets (RPNs) - a type of Petri nets that embeds reversible computation, to bounded Coloured Petri Nets (CPNs) - an extension of traditional Petri Nets, where tokens carry data values. Three reversing semantics are possible in RPNs: backtracking (reversing of the lately executed action), causal reversing (action can be reversed only when all its effects have been undone) and out of causal reversing (any previously performed action can be reversed). In this paper, we extend the RPN to CPN translation with formal proofs of correctness. Moreover, the possibility of introduction of cycles to RPNs is discussed. We analyze which type of cycles could be allowed in RPNs to ensure consistency with the current semantics. It emerged that the most interesting case related to cycles in RPNs occurs in causal semantics, where various interpretations of dependency result in different net's behaviour during reversing. Three definitions of dependence are presented and discussed. Comment: arXiv admin note: text overlap with arXiv:2101.07066 by other authors

Reversible computation deals with mechanisms for undoing the effects of actions executed by a dynamic system. This paper is concerned with reversibility in the context of Petri nets which are a general formal model of concurrent systems. A key construction we investigate amounts to adding ‘reverse’ versions of selected net transitions. Such a static modification can severely impact on the behaviour of the system, e.g., the problem of establishing whether the modified net has the same states as the original one is undecidable. We therefore concentrate on nets with finite state spaces and show, in particular, that every transition in such nets can be reversed using a suitable set of new transitions.

The notion of persistency, based on the rule "no action can disable another one" is one of the classical notions in concurrency theory. We propose two ways of generalization of this notion: the first is "no action can kill another one" and the second "no action can kill another enabled one". We study the three notions in the context of place/transition nets, the fundamental class of Petri nets. We prove that the three classes of persistency form an increased strict hierarchy. The final section of the paper deals with decision problems about persistency. We show that the set reachability problem is decidable for rational convex sets, and using this result we prove that all kinds of persistency are decidable in the class place/transition nets.