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Decidability problems in Petri nets with names and replication
, 2001
"... 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 νRN systems (RN extended with name creation ..."
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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 νRN systems (RN extended with name creation, which are Turingcomplete, 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 νRN 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 νPN (P/T nets extended with name creation), that we call pνPN, in which tokens are tuples of names. We prove that pνPN are Turing complete, and discuss how the results obtained for νRN systems can be translated to them.
Decidability results for restricted models of Petri nets with name creation and replication
, 2009
"... In previous works we defined νAPNs, an extension of P/T nets with the capability of creating and managing pure names. We proved that, though reachability is undecidable, coverability remains decidable for them. We also extended P/T nets with the capability of nets to replicate themselves, creatin ..."
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In previous works we defined νAPNs, an extension of P/T nets with the capability of creating and managing pure names. We proved that, though reachability is undecidable, coverability remains decidable for them. We also extended P/T nets with the capability of nets to replicate themselves, creating a new component, initially marked in some fixed way, obtaining gRN systems. We proved that these two extensions of P/T nets are equivalent, so that gRN systems have undecidable reachability and decidable coverability. Finally, for the class of the so called νRN systems, P/T nets with both name creation and replication, we proved that they are Turing complete, so that also coverability turns out to be undecidable. In this paper we study how can we restrict the models of νAPNs (and, therefore, gRN systems) and νRN systems in order to keep decidability of reachability and coverability, respectively. We prove that if we forbid synchronizations between the different components in a gRN system, then reachability is still decidable. The proof is done by reducing it to reachability in a class of multiset rewriting systems, similar to Recursive Petri Nets. Analogously, if we forbid name communication between the different components in a νRN system, or restrict communication to happen only for a given finite set of names, we obtain decidability of coverability.
Forward analysis for Petri nets with name creation
"... 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 νAPNs and proved that they are strictly well structured (WSTS), so that coverability and boundedn ..."
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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 νAPNs 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 GoubaultLarrecq for forward analysis for WSTS, in the case of νAPNs, 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 KarpMiller procedure that computes the cover is applicable. However, we prove that in general the cover is not computable, so that the procedure is nonterminating 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 widthboundedness.
Accelerations for the coverability set of Petri nets with names
, 2001
"... 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 νPNs and proved that they are strictly well structured (WSTS), so that coverability and boundednes ..."
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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 νPNs 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 GoubaultLarrecq for forward analysis for WSTS, in the case of νPNs, 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 KarpMiller procedure that computes the cover is applicable. However, we prove that in general the cover is not computable, so that the procedure is nonterminating 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 widthboundedness, and identify a subclass of νPN that we call dwbounded νPN, for which the cover is computable.
Decision Problems for Petri Nets with Names
, 2010
"... We prove several decidability and undecidability results for νPN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of νPN strictly s ..."
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We prove several decidability and undecidability results for νPN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of νPN strictly surpasses that of P/T nets. We prove that νPN are Well Structured Transition Systems. In particular, we obtain decidability of coverability and termination, so that the expressive power of Turing machines is not reached. Moreover, they are strictly Well Structured, so that the boundedness problem is also decidable. We consider two properties, widthboundedness and depthboundedness, that factorize boundedness. Widthboundedness has already been proved to be decidable. We prove here undecidability of depthboundedness. Finally, we obtain Ackermannhardness results for all our decidable decision problems.
From Specification to Execution
"... title = {Interacting services: From specification to executio}, jounal = {Data \ & Knowledge Engineering}, year = {2009}, volume = 68, number = 10, pages = {946‐‐972}, doi = {10.1016/j.datak.2009.04.003}, ..."
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title = {Interacting services: From specification to executio}, jounal = {Data \ & Knowledge Engineering}, year = {2009}, volume = 68, number = 10, pages = {946‐‐972}, doi = {10.1016/j.datak.2009.04.003},
Formal Verification of Petri Nets with Names
"... Abstract. Petri nets with name creation and management have been recently introduced so as to make Petri nets able to model the dynamics of (distributed) systems equipped with channels, cyphering keys, or computing boundaries. While traditional formal properties such as boundedness, coverability, an ..."
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Abstract. Petri nets with name creation and management have been recently introduced so as to make Petri nets able to model the dynamics of (distributed) systems equipped with channels, cyphering keys, or computing boundaries. While traditional formal properties such as boundedness, coverability, and reachability, have been thoroughly studied for this class of Petri nets, formal verification against rich temporal properties has not been investigated so far. In this paper, we attack this verification problem. We introduce sophisticated variants of firstorder µcalculus to specify rich properties that simultaneously account for the system dynamics and the names present in its states. We then analyse the (un)decidability boundaries for the verification of such logics, by considering different notions of boundedness. Notably, our decidability results are obtained via a translation to datacentric dynamic systems, a recently devised framework for the formal specification and verification of business processes working over relational database with constraints. In this light, our results contribute to the crossfertilization between areas that have not been extensively related so far. 1
Depth boundedness in multiset rewriting systems with name binding
, 2010
"... In this paper we consider νMSR, a formalism that combines the two main existing approaches for multiset rewriting, namely MSR and CMRS. In νMSR we rewrite multisets of atomic formulae, in which some names may be restricted. νMSR are Turing complete. In particular, a very straightforward encodin ..."
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In this paper we consider νMSR, a formalism that combines the two main existing approaches for multiset rewriting, namely MSR and CMRS. In νMSR we rewrite multisets of atomic formulae, in which some names may be restricted. νMSR are Turing complete. In particular, a very straightforward encoding of πcalculus process can be done. Moreover, pνPN, an extension of Petri nets in which tokens are tuples of pure names, are equivalent to νMSR. We know that the monadic subclass of νMSR is a Well Structured Transition System. Here we prove that depthbounded νMSR, that is, νMSR systems for which the interdependance of names is bounded, are also Well Structured, by following the analogous steps to those followed by R. Meyer in the case of the πcalculus. As a corollary, also depthbounded pνPN are WSTS, so that coverability is decidable for them.