Alternating Vector Addition Systems with States

Courtois, Jean-Baptiste; Schmitz, Sylvain

doi:10.1007/978-3-662-44522-8_19

Cited by 21 publications

(41 citation statements)

References 31 publications

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“…Rackoff's technique has successfully been employed to prove tight upper bounds for the coverability problem in VAS and extensions [7,3,6,13,12]. However, the technique does not readily generalise to more complex classes of well-structured transition systems, e.g.…”

Section: Discussionmentioning

confidence: 99%

“…We turn to demonstrating how easily our new proof of the doubly-exponential bound for the backward coverability algorithm on VAS can be extended to derive optimal bounds for top-down alternating branching VAS: Tower in general [13] and 2ExpTime with alternation only [6].…”

Section: B Top-down Tree Coverabilitymentioning

confidence: 99%

“…A non-deterministic algorithm can then simply look for such a witness using only exponential space. The same general technique has since been extended to prove tight complexity upper bounds for coverability in numerous extensions of VASs [7,3,6,13,12]. It is however less clear how to adapt the technique for more general systems, where for instance the notion of dimension is absent or more involved.…”

Section: Introductionmentioning

confidence: 99%

“…B and C the top-down and bottom-up coverability problems in alternating branching VAS. In each case, we provide an instance of the generic backward algorithm that solves the problem, and sketch why its running time matches the known optimal complexities [7,6,13].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Ideal View on Rackoff’s Coverability Technique

Lazić

Schmitz

2015

Lecture Notes in Computer Science

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Abstract. Rackoff's small witness property for the coverability problem is the standard means to prove tight upper bounds in vector addition systems (VAS) and many extensions. We show how to derive the same bounds directly on the computations of the VAS instantiation of the generic backward coverability algorithm. This relies on a dual view of the algorithm using ideal decompositions of downwards-closed sets, which exhibits a key structural invariant in the VAS case. The same reasoning readily generalises to several VAS extensions.

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Section: Discussionmentioning

confidence: 99%

Section: B Top-down Tree Coverabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Ideal View on Rackoff’s Coverability Technique

Lazić

Schmitz

2015

Lecture Notes in Computer Science

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“…the number of nodes, of the longest simple path from the root to a leaf. An alternating VASS (AVASS) [17] is a tuple A = (Q , r, R 1 , R 2 ) such that:…”

Section: Alternating Vassmentioning

confidence: 99%

On the Complexity of Resource-Bounded Logics

Alechina

Bulling

Demri

et al. 2016

Lecture Notes in Computer Science

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We revisit decidability results for resource-bounded logics and use decision problems on vector addition systems with states (VASS) in order to establish complexity characterisations of (decidable) model checking problems. We show that the model checking problem for the logic RB±ATL is 2exptime-complete by using recent results on alternating VASS (and in exptime when the number of resources is bounded). Moreover, we establish that the model checking problem for RBTL is expspace-complete. The problem is decidable and of the same complexity for RBTL * , proving a new decidability result as a by-product of the approach. When the number of resources is bounded, the problem is in pspace. We also establish that the model checking problem for RB±ATL * , the extension of RB±ATL with arbitrary path formulae, is decidable by a reduction to parity games for single-sided VASS (a variant of alternating VASS). Furthermore, we are able to synthesise values for resource parameters. Hence, the paper establishes formal correspondences between model checking problems for resource-bounded logics advocated in the AI literature and decision problems on alternating VASS, paving the way for more applications and cross-fertilizations.

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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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Alternating Vector Addition Systems with States

Cited by 21 publications

References 31 publications

The Ideal View on Rackoff’s Coverability Technique

The Ideal View on Rackoff’s Coverability Technique

On the Complexity of Resource-Bounded Logics

Round-Bounded Control of Parameterized Systems

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