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Comparing the Expressive Power of Wellstructured Transition Systems
, 2007
"... We compare the expressive power of a class of wellstructured transition systems that includes relational automata, Petri nets, lossy channel systems, and constrained multiset rewriting systems. For each one of these models we study the class of languages generated by labelled transition systems des ..."
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Cited by 13 (4 self)
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We compare the expressive power of a class of wellstructured transition systems that includes relational automata, Petri nets, lossy channel systems, and constrained multiset rewriting systems. For each one of these models we study the class of languages generated by labelled transition systems describing their semantics. We consider here two types of accepting conditions: coverability and reachability of a given configuration. In both cases we obtain a strict hierarchy in which constrained multiset rewriting systems is the the most expressive model.
A Classification of the Expressive Power of Wellstructured Transition Systems
"... Abstract. We compare the expressive power of a class of wellstructured transition systems that includes relational automata, (extensions of) Petri nets, lossy channel systems, constrained multiset rewriting systems, and data nets. For each one of these models we study the class of languages generat ..."
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Cited by 6 (1 self)
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Abstract. We compare the expressive power of a class of wellstructured transition systems that includes relational automata, (extensions of) Petri nets, lossy channel systems, constrained multiset rewriting systems, and data nets. For each one of these models we study the class of languages generated by labelled transition systems describing their semantics. We consider here two types of accepting conditions: coverability and reachability of a fixed a priori configuration. In both cases we obtain a strict hierarchy in which constrained multiset rewriting systems is the the most expressive model.
A languagebased comparison of extensions of petri nets with and without wholeplace operations
 IN DEDIU, A.H., IONESCU, A.M., MARTÍNVIDE, C., EDS.: LATA. VOLUME 5457 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2009
"... We use language theory to study the relative expressiveness of infinitestate models laying in between finite automata and Turing machines. We focus here our attention on well structured transition systems that extend Petri nets. For these models, we study the impact of wholeplace operations like ..."
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Cited by 5 (1 self)
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We use language theory to study the relative expressiveness of infinitestate models laying in between finite automata and Turing machines. We focus here our attention on well structured transition systems that extend Petri nets. For these models, we study the impact of wholeplace operations like transfers and resets on nets with indistinguishable tokens and with tokens that carry data over an infinite domain. Our measure of expressiveness is defined in terms of the class of languages recognized by a given model using coverability of a configuration as accepting condition.
Ordinal Theory for Expressiveness of Well Structured Transition Systems
"... Abstract. To the best of our knowledge, we characterize for the first time the importance of resources (counters, channels, alphabets) when measuring expressiveness of WSTS. We establish, for usual classes of wpos, the equivalence between the existence of order reflections (nonmonotonic order embedd ..."
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Abstract. To the best of our knowledge, we characterize for the first time the importance of resources (counters, channels, alphabets) when measuring expressiveness of WSTS. We establish, for usual classes of wpos, the equivalence between the existence of order reflections (nonmonotonic order embeddings) and the simulations with respect to coverability languages. We show that the nonexistence of order reflections can be proved by the computation of order types. This allows us to solve some open problems and to unify the existing proofs of the WSTS classification.
The OrdinalRecursive Complexity of TimedArc Petri Nets, Data Nets, and Other Enriched Nets
, 2013
"... Abstract—We show how to reliably compute fastgrowing functions with timedarc Petri nets and data nets. This construction provides ordinalrecursive lower bounds on the complexity of the main decidable properties (safety, termination, regular simulation, etc.) of these models. Since these new lower ..."
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Abstract—We show how to reliably compute fastgrowing functions with timedarc Petri nets and data nets. This construction provides ordinalrecursive lower bounds on the complexity of the main decidable properties (safety, termination, regular simulation, etc.) of these models. Since these new lower bounds match the upper bounds that one can derive from wqo theory, they precisely characterise the computational power of these socalled “enriched ” nets. Index Terms—Complexity theory, fastgrowing hierarchy, formal verification, Petri nets, wellstructured systems I.
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.
and Timed Petri Nets
, 2010
"... Abstract. WellStructured Transitions Systems (WSTS) constitute a generic class of infinitestate systems for which several properties like coverability remain decidable. The family of coverability languages that they generate is an appropriate criterium for measuring their expressiveness. Here we e ..."
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Abstract. WellStructured Transitions Systems (WSTS) constitute a generic class of infinitestate systems for which several properties like coverability remain decidable. The family of coverability languages that they generate is an appropriate criterium for measuring their expressiveness. Here we establish that Petri Data nets (PDNs) and Timed Petri nets (TdPNs), two powerful classes of WSTS are equivalent w.r.t this criterium. 1
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"... Communicated by (xxxxxxxxxx) The minimal coverability set (MCS) of a Petri net is a finite representation of the downwardclosure of its reachable markings. The minimal coverability set allows to decide several important problems like coverability, semiliveness, place boundedness, etc. The classica ..."
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Communicated by (xxxxxxxxxx) The minimal coverability set (MCS) of a Petri net is a finite representation of the downwardclosure of its reachable markings. The minimal coverability set allows to decide several important problems like coverability, semiliveness, place boundedness, etc. The classical algorithm to compute the MCS constructs the Karp&Miller (KM) tree [8]. Unfortunately the KM tree is often huge, even for small nets. An improvement of this KM algorithm is the Minimal Coverability Tree (MCT) algorithm [1], which has been introduced nearly 20 years ago, and implemented since then in several tools such as Pep [7]. Unfortunately, we show in this paper that the MCT is flawed: it might compute an underapproximation of the reachable markings. We propose a new solution for the efficient computation of the MCS of Petri nets. Our algorithm is based on new ideas, and the experimental results show that it behaves much better in practice than the KM algorithm.