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Name Creation vs. Replication in Petri Net Systems

100%

Rosa-Velardo F. , de Frutos-Escrig D.

2008

tom Vol. 88, nr 3

329-356

We study the relationship between name creation and replication in a setting of infinitestate communicating automata. By name creation we mean the capacity of dynamically producing pure names, with no relation between them other than equality or inequality. By replication we understand the ability of systems of creating new parallel identical threads, that can synchronize with each other. We have developed our study in the framework of Petri nets, by considering several extensions of P/T nets. In particular, we prove that in this setting name creation and replication are equivalent, but only when a garbage collection mechanism is added for idle threads. However, when simultaneously considering both extensions the obtained model is, a bit surprisingly, Turing complete and therefore, more expressive than when considered separately.

Safety and Soundness for Priced Resource : Constrained Workflow Nets

100%

Martos-Salgado M. , Rosa-Velardo F.

Fundamenta Informaticae

2014

tom Vol. 131, nr 1

55--80

We extend workflow Petri nets (wf-nets) with discrete prices, by associating a price to the execution of a transition and to the storage of tokens. We first define the safety and the soundness problems for priced wf-nets. A priced wf-net is safe if no execution costs more than a given budget. The soundness problem is that of deciding whether the workflow can always terminate properly, where in the priced setting “properly” also means that the execution does not cost more than a given threshold. Then, we study safety and soundness of resource-constrained workflow nets (rcwf-nets), an extension of wf-nets for the modeling of concurrent executions of a workflow, sharing some global resources. We develop a framework in which to study safety and soundness for priced rcwf-nets, that is parametric on the cost model. Then, that framework is instantiated, obtaining the cases in which the sum, the maximum, the average and the discounted sum of the prices of all instances are considered. We study the decidability and the complexity of these properties, together with their relation.

Decidability Problems in Petri Nets with Names and Replication

100%

Rosa-Velardo F. , Frutos-Escrig D. d.

tom Vol. 105, nr 3

291-317

In this paper we study decidability of several extensions of P/T nets with name creation and/or replication. In particular, we study how to restrict the models of RN systems (P/T nets extended with replication, for which reachability is undecidable) and í-RN systems (RN extendedwith name creation, which are Turing-complete, so that coverability is undecidable), in order to obtain decidability of reachability and coverability, respectively. We prove that if we forbid synchronizations between the different components in a RN system, then reachability is still decidable. Similarly, if we forbid name communication between the different components in a &nuRN system, or restrict communication so that it is allowed only for a given finite set of names, we obtain decidability of coverability. Finally, we consider a polyadic version of ν-PN (P/T nets extended with name creation), that we call pν-PN, in which tokens are tuples of names. We prove that pν-PN are Turing complete, and discuss how the results obtained for ν-RN systems can be translated to them.

Accelerations for the Coverability Set of Petri Nets with Names

80%

Rosa-Velardo F. , Martos-Salgado M. , Frutos-Escrig D. d.

2011

tom Vol. 113, nr 3/4

313-341

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 -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 -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 -PN that we call dw-bounded v-PN, for which the cover is computable.