A unified view of parameterized verification of abstract models of broadcast communication

Delzanno, Giorgio

doi:10.1007/s10009-016-0412-7

Cited by 7 publications

(3 citation statements)

References 93 publications

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“…Those properties make VASS and their extensions a prime choice for reasoning about and modelling concurrent, distributed and parametrised systems, see e.g. the recent surveys by Abdulla and Delzanno [AD16,Del16].…”

Section: Introductionmentioning

confidence: 99%

Affine Extensions of Integer Vector Addition Systems with States

Blondin¹,

Haase²,

Mazowiecki³

et al. 2021

Logical Methods in Computer Science

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We study the reachability problem for affine $\mathbb{Z}$-VASS, which are integer vector addition systems with states in which transitions perform affine transformations on the counters. This problem is easily seen to be undecidable in general, and we therefore restrict ourselves to affine $\mathbb{Z}$-VASS with the finite-monoid property (afmp-$\mathbb{Z}$-VASS). The latter have the property that the monoid generated by the matrices appearing in their affine transformations is finite. The class of afmp-$\mathbb{Z}$-VASS encompasses classical operations of counter machines such as resets, permutations, transfers and copies. We show that reachability in an afmp-$\mathbb{Z}$-VASS reduces to reachability in a $\mathbb{Z}$-VASS whose control-states grow linearly in the size of the matrix monoid. Our construction shows that reachability relations of afmp-$\mathbb{Z}$-VASS are semilinear, and in particular enables us to show that reachability in $\mathbb{Z}$-VASS with transfers and $\mathbb{Z}$-VASS with copies is PSPACE-complete. We then focus on the reachability problem for affine $\mathbb{Z}$-VASS with monogenic monoids: (possibly infinite) matrix monoids generated by a single matrix. We show that, in a particular case, the reachability problem is decidable for this class, disproving a conjecture about affine $\mathbb{Z}$-VASS with infinite matrix monoids we raised in a preliminary version of this paper. We complement this result by presenting an affine $\mathbb{Z}$-VASS with monogenic matrix monoid and undecidable reachability relation.

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Section: Introductionmentioning

confidence: 99%

Affine Extensions of Integer Vector Addition Systems with States

Blondin¹,

Haase²,

Mazowiecki³

et al. 2021

Logical Methods in Computer Science

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“…A much more complete survey of di erent parameterised models and verification methods that can be applied to concurrent and distributed systems with broadcast communication based on transition systems is presented in [Delzanno, 2016].…”

Section: Arbitrary Number Of Identical Resourcesmentioning

confidence: 99%

Discrete Parameters in Petri Nets

David

Jard

Lime

et al. 2015

Application and Theory of Petri Nets and Concurrency

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Short abstract:With the aim of increasing the modelling capability of Petri nets, we suggest that models involve parameters to represent the weights of arcs, or the number of tokens in places. We consider the property of coverability of markings. Two general questions arise, the universal and the existential one: "Is there a parameter value for which the property is satisfied?" and "Does the property hold for all possible values of the parameters". We show that these issues are undecidable in the general case. Therefore, we also define subclasses of parameterised nets, depending on whether the parameters are used on places, input or output arcs of transitions. For some classes, we prove that universal and existential coverability become decidable, making these classes more usable in practice. To complete this study, we prove that those problems are ExpSpace-complete. We also address a problem of parameter synthesis, that is computing the set of values for the parameters such that a given marking is coverable in the instantiated net. Restricting parameters to only input weights (preT-PPNs) provides a downward-closed structure to the solution set. We therefore invoke a result for the representation of upward closed set from Valk and Jantzen. The condition to use this procedure is equivalent to decide the universal coverability. We also propose an adaptation of this reasoning to the case of parameters used only as output weights (postT-PPNs). In this case, the condition to use this procedure can be reduced to the decidability of the existential coverability. Finally, we broaden this study by establishing decision frontiers through the study of existential and universal reachability.Keywords: Petri nets -Parameters -Synthesis -Decidability -Complexity -CoverabilityReachability 6 Réseaux de Petri à Paramètres DiscretsRésumé court : Afin de permettre une modélisation plus souple des systèmes, nous proposons d'étendre les réseaux de Petri par des paramètres discrets représentant le poids des arcs ou le nombre de jetons présents dans les places. Dans ce modèle, tout problème de décision peut être décliné sous deux versions, une universelle, demandant si la propriété considérée est vraie quelles que soient les valeurs que prennent les paramètres et une existentielle, qui s'interroge sur l'existence d'une valeur pour les paramètres telle que la propriété soit satisfaite. Concernant la couverture, nous montrons que ces deux problèmes sont indécidables dans le cas général. Nous introduisons donc des sous classes syntaxiques basées sur la restriction des paramètres aux places, aux arcs en sortie ou aux arcs en entrée des transitions. Dans ces di érents cas, nous montrons que la couverture existentielle et universelle sont décidables et EXPSPACE-complètes. Nous étudions alors le problème de la synthèse de paramètres qui s'intéresse à calculer l'ensemble des valeurs de paramètres telles que la propriété considérée soit vraie. Sur les sous classes introduites, concernant la couverture, nous montrons que les ensembles solutions ...

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Section: Introductionmentioning

confidence: 99%

Affine Extensions of Integer Vector Addition Systems with States

Blondin,

Haase,

Mazowiecki

et al. 2019

Preprint

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We study the reachability problem for affine Z-VASS, which are integer vector addition systems with states in which transitions perform affine transformations on the counters. This problem is easily seen to be undecidable in general, and we therefore restrict ourselves to affine Z-VASS with the finite-monoid property (afmp-Z-VASS). The latter have the property that the monoid generated by the matrices appearing in their affine transformations is finite. The class of afmp-Z-VASS encompasses classical operations of counter machines such as resets, permutations, transfers and copies. We show that reachability in an afmp-Z-VASS reduces to reachability in a Z-VASS whose control-states grow linearly in the size of the matrix monoid. Our construction shows that reachability relations of afmp-Z-VASS are semilinear, and in particular enables us to show that reachability in Z-VASS with transfers and Z-VASS with copies is PSPACE-complete. We then focus on the reachability problem for affine Z-VASS with monogenic monoids: (possibly infinite) matrix monoids generated by a single matrix. We show that, in a particular case, the reachability problem is decidable for this class, disproving a conjecture about affine Z-VASS with infinite matrix monoids we raised in a preliminary version of this paper. We complement this result by presenting an affine Z-VASS with monogenic matrix monoid and undecidable reachability relation.

show abstract

A unified view of parameterized verification of abstract models of broadcast communication

Cited by 7 publications

References 93 publications

Affine Extensions of Integer Vector Addition Systems with States

Affine Extensions of Integer Vector Addition Systems with States

Discrete Parameters in Petri Nets

Affine Extensions of Integer Vector Addition Systems with States

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