Reachability Games on Extended Vector Addition Systems with States

Brázdil, Tomǎš; Jancar, Petr; Kučera, Antonín

doi:10.1007/978-3-642-14162-1_40

Cited by 82 publications

(156 citation statements)

References 33 publications

(67 reference statements)

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“…can then be envisioned, and correspond to conditions that must be satisfied by all the branches of a deduction tree. As shown by Abdulla et al [2], such asymmetric games are closely related to multi-dimensional energy games [8,6], see Section 5.…”

Section: Deduction Semantics Given An Avass Its Semantics Is Definementioning

confidence: 86%

“…Brázdil, Jančar, and Kučera [6] show in the context of Z-reachability games that this problem is ExpSpace-hard, and in (d − 1)-ExpTime when the dimension d is fixed. Our 2-ExpTime lower bound in Proposition 4.1 is the best known lower bound for this problem, leaving a large complexity gap.…”

Section: 22mentioning

confidence: 99%

“…Multi-dimensional Energy Games. Abdulla et al [2] have shown the equivalence of AVASS games with the (multi-dimensional) energy games of Brázdil et al [6] and Chatterjee et al [8], where the asymmetry between Controller and Environment is not enforced in the structure of the AVASS or in restricted unary rules for Environment: in such a game, Environment can use arbitrary unary rules. This would lead to an undecidable state reachability game when played on the Q × N d arena [1], but energy games are played instead over Q×Z d -which means that unary rules can be applied even if they yield some negative vector components.…”

Section: Energy Gamesmentioning

confidence: 99%

“…. remain non-negative (positive in [6]). Such games are motivated by the synthesis of controllers able to ensure that quantitative values (represented by the integer vectors) are maintained above some critical values.…”

Section: Energy Gamesmentioning

confidence: 99%

“…Surprisingly, this is not really the case: if there is indeed a large number of denominations (e.g. B-VASS games [23], Z-reachability games [6], multi-dimensional energy games [8]), Abdulla, Mayr, Sangnier, and Sproston [2] noted last year that they all defined essentially the same asymmetric class of games, where one player is restricted and cannot update the vector values.…”

Section: Introductionmentioning

confidence: 99%

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Alternating Vector Addition Systems with States

Courtois

Schmitz

2014

Mathematical Foundations of Computer Science 2014

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Abstract. Alternating vector addition systems are obtained by equipping vector addition systems with states (VASS) with 'fork' rules, and provide a natural setting for infinite-arena games played over a VASS. Initially introduced in the study of propositional linear logic, they have more recently gathered attention in the guise of multi-dimensional energy games for quantitative verification and synthesis.We show that establishing who is the winner in such a game with a state reachability objective is 2-ExpTime-complete. As a further application, we show that the same complexity result applies to the problem of whether a VASS is simulated by a finite-state system.

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Section: Deduction Semantics Given An Avass Its Semantics Is Definementioning

confidence: 86%

Section: 22mentioning

confidence: 99%

Section: Energy Gamesmentioning

confidence: 99%

Section: Energy Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Alternating Vector Addition Systems with States

Courtois

Schmitz

2014

Mathematical Foundations of Computer Science 2014

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Round-Bounded Control of Parameterized Systems

Bollig

Lehaut

Sznajder

2018

Automated Technology for Verification and Analysis

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We consider systems with unboundedly many processes that communicate through shared memory. In that context, simple verification questions have a high complexity or, in the case of pushdown processes, are even undecidable. Good algorithmic properties are recovered under round-bounded verification, which restricts the system behavior to a bounded number of round-robin schedules. In this paper, we extend this approach to a game-based setting. This allows one to solve synthesis and control problems and constitutes a further step towards a theory of languages over infinite alphabets.

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Parameterized Synthesis for Fragments of First-Order Logic Over Data Words

Bérard¹,

Bollig²,

Lehaut³

et al. 2020

Lecture Notes in Computer Science

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We study the synthesis problem for systems with a parameterized number of processes. As in the classical case due to Church, the system selects actions depending on the program run so far, with the aim of fulfilling a given specification. The difficulty is that, at the same time, the environment executes actions that the system cannot control. In contrast to the case of fixed, finite alphabets, here we consider the case of parameterized alphabets. An alphabet reflects the number of processes, which is static but unknown. The synthesis problem then asks whether there is a finite number of processes for which the system can satisfy the specification. This variant is already undecidable for very limited logics. Therefore, we consider a first-order logic without the order on word positions. We show that even in this restricted case synthesis is undecidable if both the system and the environment have access to all processes. On the other hand, we prove that the problem is decidable if the environment only has access to a bounded number of processes. In that case, there is even a cutoff meaning that it is enough to examine a bounded number of process architectures to solve the synthesis problem. Partly supported by ANR FREDDA (ANR-17-CE40-0013).

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Reachability Games on Extended Vector Addition Systems with States

Cited by 82 publications

References 33 publications

Alternating Vector Addition Systems with States

Alternating Vector Addition Systems with States

Round-Bounded Control of Parameterized Systems

Parameterized Synthesis for Fragments of First-Order Logic Over Data Words

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