Properties of Distributed Timed-Arc Petri Nets (original) (raw)

Decidability of Properties of Timed-Arc Petri Nets

Lecture Notes in Computer Science, 2000

Timed-arc Petri nets (TAPN's) are not Turing powerful, because, in particular, they cannot simulate a counter with zero testing. Thus, we could think that this model does not increase significantly the expressiveness of untimed Petri nets. But this is not true; in a previous paper we have shown that the differences between them are big enough to make the reachability problem undecidable. On the other hand, coverability and boundedness are proved now to be decidable. This fact is a consequence of the close interrelationship between TAPN's and transfer nets, for which similar results have been recently proved. Finally, we see that if dead tokens are defined as those that cannot be used for firing any transition in the future, we can detect these kind of tokens in an effective way.

The Confluence Property for Petri Nets and its Applications

2006

A Petri net is confluent if its firing relation is confluent, i.e., for any two reachable markings there exists a marking reachable from both of them. We prove that confluence is a decidable property for Petri nets and it is preserved by asynchronous parallel composition. Applications to Petri net structural transformations and term rewriting systems are then pointed out.

Flow-Invariant Sets with Respect to the Markings of Timed Continuous Petri Nets

Conference on Decision and Control, 2005

The paper investigates the existence of flow-invariant sets with respect to the marking of a timed continuous Petri net (TCPN) with infinite server semantics. Such a set has the property that for any initial marking belonging to the set, the marking at any moment in the evolution of the net also belongs to the set. Thus, the traditional concept of marking invariance used in PN theory, which refers to a set of places, is complemented in the sharper sense of the individual monitoring of each place. We take into consideration several types of bounded flow-invariant sets. The join-free TCPNs are treated separately from TCPNs with joins as allowing the development of supplementary investigation tools. Subsidiary to our results we give a consistent and rigorous mathematical proof for the nonnegativeness of the marking in TCPNs.

Continuous Reachability for Unordered Data Petri Nets is in PTime

Lecture Notes in Computer Science, 2019

Unordered data Petri nets (UDPN) are an extension of classical Petri nets with tokens that carry data from an infinite domain and where transitions may check equality and disequality of tokens. UDPN are well-structured, so the coverability and termination problems are decidable, but with higher complexity than for Petri nets. On the other hand, the problem of reachability for UDPN is surprisingly complex, and its decidability status remains open. In this paper, we consider the continuous reachability problem for UDPN, which can be seen as an over-approximation of the reachability problem. Our main result is a characterization of continuous reachability for UDPN and polynomial time algorithm for solving it. This is a consequence of a combinatorial argument, which shows that if continuous reachability holds then there exists a run using only polynomially many data values.

Linear time analysis of properties of conflict-free and general Petri nets

Theoretical Computer Science, 2011

We introduce the notion of T -path within Petri nets, and propose a simple approach, based on previous work developed for directed hypergraphs, in order to determine structural properties of nets; in particular, we study the relationships between T -paths in a Petri net and firable sequences of transitions.

On interleaving in {P,A}-Time Petri nets with strong semantics

This paper deals with the reachability analysis of {P,A}-Time Petri nets ({P,A}-TPN in short) in the context of strong semantics. It investigates the convexity of the union of state classes reached by different interleavings of the same set of transitions. In [6], the authors have considered the T-TPN model and its Contracted State Class Graph (CSCG) [7] and shown that this union is not necessarily convex. They have however established some sufficient conditions which ensure convexity. This paper shows that for the CSCG of {P,A}-TPN, this union is convex and can be computed without computing intermediate state classes. These results allow to improve the forward reachability analysis by agglomerating, in the same state class, all state classes reached by different interleavings of the same set of transitions (abstraction by convex-union).

Accelerations for the Coverability Set of Petri Nets with Names

Fundamenta Informaticae, 2011

Pure names are identifiers with no relation between them, except equality and inequality. In previous works we have extended P/T nets with the capability of creating and managing pure names, obtaining ν-PNs and proved that they are strictly well structured (WSTS), so that coverability and boundedness are decidable. Here we use the framework recently developed by Finkel and Goubault-Larrecq for forward analysis for WSTS, in the case of ν-PNs, to compute the cover, that gives a good over approximation of the set of reachable markings. We prove that the least complete domain containing the set of markings is effectively representable. Moreover, we prove that in the completion we can compute least upper bounds of simple loops. Therefore, a forward Karp-Miller procedure that computes the cover is applicable. However, we prove that in general the cover is not computable, so that the procedure is non-terminating in general. As a corollary, we obtain the analogous result for Transfer Data nets and Data Nets. Finally, we show that a slight modification of the forward analysis yields decidability of a weak form of boundedness called width-boundedness, and identify a subclass of ν-PN that we call dw-bounded ν-PN, for which the cover is computable.

Undecidability of coverability and boundedness for timed-arc Petri nets with invariants

Proc. of MEMICS, 2009

Timed-Arc Petri Nets (TAPN) is a well studied extension of the classical Petri net model where tokens are decorated with real numbers that represent their age. Unlike reachability, which is known to be undecidable for TAPN, boundedness and coverability remain decidable. The model is supported by a recent tool called TAPAAL which, among others, further extends TAPN with invariants on places in order to model urgency. The decidability of boundedness and coverability for this extended model has not yet been considered. We present a reduction from two-counter Minsky machines to TAPN with invariants to show that both the boundedness and coverability problems are undecidable.