Model Checking Succinct and Parametric One-Counter Automata

Göller, Stefan; Haase, Christoph; Ouaknine, Joël; Worrell, James

doi:10.1007/978-3-642-14162-1_48

Cited by 32 publications

(61 citation statements)

References 22 publications

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“…The same reduction shows that CTL model checking on succinct one-counter automata reduces to Büchi games on onecounter graphs. In [5], CTL model checking on succinct one-counter automata was shown to be EXPSPACE-complete, hence one-counter games with a Büchi winning condition are also EXPSPACE-hard. …”

Section: Expspace-hardness Of Büchi Gamesmentioning

confidence: 99%

Reachability in Succinct One-Counter Games

Hunter

2015

Lecture Notes in Computer Science

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We consider the reachability problem on transition systems corresponding to succinct one-counter machines, that is, machines where the counter is incremented or decremented by a value given in binary. PreliminariesWe are interested in reachability problems on transition graphs defined by onecounter machines where:• The counter may take any integer value (including negative values);• The counter is incremented or decremented by binary weights;• Additional transitions are available to the machine if the counter does or does not have value 0.Previous work [1,2] has considered other variations on these initial assumptions. Formally, a transition graph of a one-counter machine (or one-counter graph) is given by a tuple (V, V ∃ , E, E 0 , E =0 , q 0 , w) where V is a finite set of states; V ∃ ⊆ V are the states of Eve (V \ V ∃ are the states of Adam);is the set of edges (de)activated at 0); q 0 ∈ V is the initial state; and w : E → Z is the weight function. The (infinite) unweighted arena defined by such a tuple has:• For every e = (v, v ′ ) ∈ E 0 an edge from (v, 0) to (v ′ , 0), and Reachability problemsWe are interested in the following reachability problems listed in increasing order of difficulty. They are all known to be in EXPSPACE and EXPTIME-hard. Finite memory strategies suffice for all but parity games.✩ Work supported by ERC inVEST project

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Section: Expspace-hardness Of Büchi Gamesmentioning

confidence: 99%

Reachability in Succinct One-Counter Games

Hunter

2015

Lecture Notes in Computer Science

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“…The former problem was proved EXPSPACE-complete in [GHOW10], and PSPACEcomplete over unitary one-counter automata in [GL10]. The reduction is rather straightforward, by reinforcing the CTL formula in order to enforce nonnegative value of the accumulated weight all along the paths.…”

Section: Wctl Rfmentioning

confidence: 99%

“…Our proof closely follows the ideas of [GHOW10] and [DG09]: we apply the same transformation as for WCTL, reducing our weighted Kripke structure into a unitary one-counter automaton. We then plug at each state a module (as displayed on Fig.…”

Section: Decidability Of Wltl Rfmentioning

confidence: 99%

“…Models with both positive and negative weights have also been studied, but mostly qualitative behaviours alone have been analyzed (this is the case in counter automatasee [HKOW09,GHOW10,Haa12] for recent references), or quantitative constraints have been analyzed (in weighted Kripke structures or games [CDHR10,CRR12]). Mixing qualitative logical properties and quantitative constraints has only poorly been addressed so far, and many works only consider specifications given as a conjunction of a qualitative logical property and a quantitative constraint: this is for instance the case of optimal reachability, mean-payoff parity games [BMOU11], energy parity games [CD12], mean-payoff LTL synthesis [BBFR13].…”

Section: Introductionmentioning

confidence: 99%

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Quantitative Verification of Weighted Kripke Structures

Bouyer

Gardy

Markey

2014

Automated Technology for Verification and Analysis

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Abstract. Extending formal verification techniques to handle quantitative aspects, both for the models and for the properties to be checked, has become a central research topic over the last twenty years. Following several recent works, we study model checking for (one-dimensional) weighted Kripke structures with positive and negative weights, and temporal logics constraining the total and/or average weight. We prove decidability when only accumulated weight is constrained, while allowing average-weight constraints alone already is undecidable.

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“…Precise complexity of reachability and many other problems of this model have been recently obtained in [12,11]. We have adapted some of the techniques used in [12,11], in particular the use of [16,Lemma 42].…”

Section: Introductionmentioning

confidence: 99%

Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

Praveen

2012

Algorithmica

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Abstract. The coverability and boundedness problems for Petri nets are known to be Expspacecomplete. Given a Petri net, we associate a graph with it. With the vertex cover number k of this graph and the maximum arc weight W as parameters, we show that coverability and boundedness are in ParaPspace. This means that these problems can be solved in space O (ef (k, W )poly(n)), where ef (k, W ) is some exponential function and poly(n) is some polynomial in the size of the input. We then extend the ParaPspace result to model checking a logic that can express some generalizations of coverability and boundedness.

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Model Checking Succinct and Parametric One-Counter Automata

Cited by 32 publications

References 22 publications

Reachability in Succinct One-Counter Games

Reachability in Succinct One-Counter Games

Quantitative Verification of Weighted Kripke Structures

Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

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