Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

Praveen, M.

doi:10.1007/s00453-012-9687-6

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Any vertex cover of G(N ) should include all vertices that have self loops. It was shown in [18,17] that benefit depth and vertex cover number bring down the complexity of coverability and boundedness in general Petri nets from exponential space-complete [19] to ParaPspace.…”

Section: Parametersmentioning

confidence: 99%

Parameterized Complexity Results for 1-safe Petri Nets

Praveen

Lodaya

2011

CONCUR 2011 – Concurrency Theory

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We associate a graph with a 1-safe Petri net and study the parameterized complexity of various problems with parameters derived from the graph. With treewidth as the parameter, we give W[1]-hardness results for many problems about 1-safe Petri nets. As a corollary, this proves a conjecture of Downey et. al. about the hardness of some graph pebbling problems. We consider the parameter benefit depth (that is known to be helpful in getting better algorithms for general Petri nets) and again give W[1]-hardness results for various problems on 1-safe Petri nets. We also consider the stronger parameter vertex cover number. Combining the well known automata-theoretic method and a powerful fixed parameter tractability (Fpt) result about Integer Linear Programming, we give a Fpt algorithm for model checking Monadic Second Order (MSO) formulas on 1-safe Petri nets, with parameters vertex cover number and the size of the formula.

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Section: Parametersmentioning

confidence: 99%

Parameterized Complexity Results for 1-safe Petri Nets

Praveen

Lodaya

2011

CONCUR 2011 – Concurrency Theory

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“…For Petri nets, the reachability problem is hard but decidable [35]. Further important problems that are specific to Petri nets and that were shown decidable are boundedness [29,38], deadlock-freeness and liveness [20] (by reduction to reachability), persistence [18], and semilinearity [22]. Hack's thesis [20] provides a comprehensive overview of problems equivalent to Petri net reachability.…”

Section: Introductionmentioning

confidence: 99%

Petri Net Reachability Graphs: Decidability Status of First Order Properties

Darondeau¹,

Demri²,

Meyer³

et al. 2012

Logical Methods in Computer Science

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Abstract. We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques.

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“…Apart from this unorthodox adaptation of [45], in the counterpart of Rackoff's proof about the induction on the dimension, we provide an induction on the dimension and on the length of the properties to be verified (see Lemma 4.4). The preliminary work [13] has already been used in [42] to obtain new complexity results. This is a genuine breakthrough comparable to [45,48,24,3].…”

Section: Introductionmentioning

confidence: 99%

On Selective Unboundedness of VASS

Demri

2010

Electron. Proc. Theor. Comput. Sci.

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Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, counter values, run lengths). Some of these features can be checked in exponential space by using Rackoff's proof or its variants, combined with Savitch's Theorem. However, the question is still open for many others, e.g., regularity detection problem and reversal-boundedness detection problem. In the paper, we introduce the class of generalized unboundedness properties that can be verified in exponential space by extending Rackoff's technique, sometimes in an unorthodox way. We obtain new optimal upper bounds, for example for place boundedness problem, reversal-boundedness detection (several variants are present in the paper), strong promptness detection problem and regularity detection. Our analysis is sufficiently refined so as to obtain a polynomial-space bound when the dimension is fixed.

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Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

Cited by 3 publications

References 25 publications

Parameterized Complexity Results for 1-safe Petri Nets

Parameterized Complexity Results for 1-safe Petri Nets

Petri Net Reachability Graphs: Decidability Status of First Order Properties

On Selective Unboundedness of VASS

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