Ordinal Theory for Expressiveness of Well Structured Transition Systems

Bonnet, Rémi; Finkel, Alain; Haddad, Serge; Rosa-Velardo, Fernando

doi:10.1007/978-3-642-19805-2_11

Cited by 11 publications

(6 citation statements)

References 16 publications

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“…The characterization of the expressive power by means of covering languages has been done for Petri nets (studied in the book of Peterson [27]), and more recently, for Well Structured Transition Systems (WSTS) [28] and for monotonic extensions of Petri nets like reset-transfer Petri nets, ν-Petri nets, unordered Petri nets [29,30]. More properties are decidable for VASS covering languages than for VASS reachability languages.…”

Section: Expressivenessmentioning

confidence: 99%

Coverability and Termination in Recursive Petri Nets

Finkel

Haddad

Khmelnitsky

2019

Application and Theory of Petri Nets and Concurrency

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In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and stack automata, most of the usual property problems are solvable but using non primitive recursive algorithms, even for coverability and termination. For almost all other extended Petri nets models containing a stack the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability and termination problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get for free a more powerful model than Petri net.

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Section: Expressivenessmentioning

confidence: 99%

Coverability and Termination in Recursive Petri Nets

Finkel

Haddad

Khmelnitsky

2019

Application and Theory of Petri Nets and Concurrency

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“…Lpν¡N etsq LpDN q has been proved using an application of ordinal theory [29] as a measure of the state space that has to be explored to solve coverability in the corresponding models. The method used in [29] based on order reflection is a generalization of the strict inclusion between Lossy Channel Systems and CMRS proved in [6]. Furthermore, in [6] it has been shown that…”

Section: Expressivenessmentioning

confidence: 99%

“…Finer grained comparisons between AWN, νNets and (fragments of) Data nets are presented in [29]. More general models of Petri nets with data are presented in [89].…”

Section: Expressivenessmentioning

confidence: 99%

Parameterized verification

Abdulla

Delzanno

2016

Int J Softw Tools Technol Transfer

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The goal of parameterized verification is to prove the correctness of a system specification regardless of the number of its components. The problem is of interest in several different areas: verification of hardware design, multithreaded programs, distributed systems, and communication protocols. The problem is undecidable in general. Solutions for restricted classes of systems and properties have been studied in areas like theorem proving, model checking, automata and logic, process algebra, and constraint solving. In this introduction to the special issue, dedicated to a selection of works from the Parameterized Verification workshop PV ’14 and PV ’15, we survey some of the works developed in this research area

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“…The strict inclusion Lpν¡N etsq LpDN q has been proved using an application of ordinal theory [29] as a measure of the state space that has to be explored to solve coverability in the corresponding models. The method used in [29] based on order reflection is a generalization of the strict inclusion between Lossy Channel Systems and CMRS proved in [6]. Furthermore, in [6] it has been shown that LpDN q LpCM RSq LpM SRpIdqq…”

Section: Expressivenessmentioning

confidence: 99%