Kamila Barylska

Reversible computation vs. reversibility in Petri nets

Abstract Petri nets are a general formal model of concurrent systems which supports both action-based and state-based modelling and reasoning. One of important behavioural properties investigated in the context of Petri nets has been reversibility, understood as the possibility of returning to the initial marking from any reachable net marking. Thus reversibility in Petri nets is a global property. Reversible computation, on the other hand, is typically a local mechanism by which a system can undo some of the executed actions. This paper is concerned with the modelling of reversible computation within Petri nets. A key idea behind the proposed construction is to add ‘reverses’ of selected transitions, and the paper discusses its different implementations. Adding reverses can severely impact on the behaviour of a Petri net. Therefore it is important, in particular, to be able to determine whether the modified net has a similar set of states as the initial one. We first prove that the problem of establishing whether the initial and modified nets have the same reachable markings is undecidable, even in the restricted case considered in this paper. We then show that the problem of checking whether the reachability sets of the two nets cover the same markings is decidable.

Reversing Transitions in Bounded Petri Nets

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 finite set of new transitions.

Reversible Computation vs. Reversibility in Petri Nets

Petri nets are a general formal model of concurrent systems which supports both action-based and state-based modelling and reasoning. One of important behavioural properties investigated in the context of Petri nets has been reversibility, understood as the possibility of returning to the initial marking from any reachable net marking. Thus reversibility in Petri nets is a global property. Reversible computation, on the other hand, is typically a local mechanism using which a system can undo some of the executed actions. This paper is concerned with the modelling of reversible computation within Petri nets. A key idea behind the proposed construction is to add ‘reverse’ versions of selected transitions. Since such a modification can severely impact on the behavior of the system, it is crucial, in particular, to be able to determine whether the modified system has a similar set of states as the original one. We first prove that the problem of establishing whether the two nets have the same reachable markings is undecidable even in the restricted case discussed in this paper. We then show that the problem of checking whether the reachability sets of the two nets cover the same markings is decidable.

Conditions for Petri Net Solvable Binary Words

A word is called Petri net solvable if it is isomorphic to the reachability graph of an unlabelled Petri net. In this paper, the class of finite, two-letter, Petri net solvable, words is studied. Two conjectures providing different characterisations of this class of words are motivated and proposed. One conjecture characterises the class in terms of pattern-matching, the other in terms of letter-counting. Several results are described which amount to a partial proof of these conjectures.

Properties of Plain, Pure, and Safe Petri Nets

A set of necessary conditions for a Petri net to be plain, pure and safe is given. Some applications of these conditions both in practice (for Petri net synthesis), and in theory (e.g., as part of a characterisation of the reachability graphs of live and safe marked graphs) are described.