Reducing the Size of NFAs by Using Equivalences and Preorders

Ilie, Lucian; Solis-Oba, Roberto; Yü, Sheng

doi:10.1007/11496656_27

Cited by 35 publications

(41 citation statements)

References 21 publications

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“…Moreover, since j ∈Ĩ no vertex in S j coversẽ. On the other hand, by our assumption in Equation (7) (u, j) ∈ S j , which along with Equation (11) implies that no vertex in S j coversẽ. Therefore, e is not covered by S. This is a contradiction to the fact that S is a vertex cover in G and therefore our assumption in Equation (7) is incorrect.…”

mentioning

confidence: 94%

“…Variants of this problem are studied for databases related applications such as distributed data mining [7], schema mapping discovery [8] and in optimizing finite automata [11]. The particular case of computing the minimum vertex cover in k-uniform k-partite (with the partition given) hypergraphs was studied by Lovász [16] who obtained a k/2 approximation for it by rounding its natural LP relaxation.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, Aharoni, Holzman and Krivelevich [1] proved a tight integrality gap of k/2 − o(1) for the LP relaxation. On the hardness side, [11] and [8] give reductions from 3SAT to it, which imply that the problem is APX-hard. However, to the best of our knowledge no better hardness of approximation was known for this problem.…”

Section: Introductionmentioning

confidence: 99%

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On the Inapproximability of Vertex Cover on k-Partite k-Uniform Hypergraphs

Guruswami

Saket

2010

Automata, Languages and Programming

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Abstract. Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. While intractable in general, it is well known that on bipartite graphs, vertex cover is polynomial time solvable. In this work, we study the natural extension of bipartite vertex cover to hypergraphs, namely finding a small vertex cover in kuniform k-partite hypergraphs, when the k-partition is given as input. For this problem Lovász [16] gave a k 2 factor LP rounding based approximation, and a matching k 2 − o(1) integrality gap instance was constructed by Aharoni et al. [1]. We prove the following results, which are the first strong hardness results for this problem (here ε > 0 is an arbitrary constant):-NP-hardness of approximating within a factor of k 4 − ε , and -Unique Games-hardness of approximating within a factor of k 2 − ε , showing optimality of Lovász's algorithm under the Unique Games conjecture. The NP-hardness result is based on a reduction from minimum vertex cover in r-uniform hypergraphs for which NP-hardness of approximating within r−1−ε was shown by Dinur et al. [5]. The Unique Games-hardness result is obtained by applying the recent results of Kumar et al. [15], with a slight modification, to the LP integrality gap due to Aharoni et al. [1]. The modification is to ensure that the reduction preserves the desired structural properties of the hypergraph.

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confidence: 94%

Section: Introductionmentioning

confidence: 99%

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On the Inapproximability of Vertex Cover on k-Partite k-Uniform Hypergraphs

Guruswami

Saket

2010

Automata, Languages and Programming

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“…While finding the minimum number of states for an NFA is PSPACE-hard, approaches have been presented [13,12] for reducing the size of an NFA directly.…”

Section: Sfa Reductionmentioning

confidence: 99%

Unbounded Model-Checking with Interpolation for Regular Language Constraints

Gange

Navas

Stuckey

et al. 2013

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We present a decision procedure for the problem of, given a set of regular expressions R1, . . . , Rn, determining whether R = R1 ∩ · · · ∩ Rn is empty. Our solver, revenant, finitely unrolls automata for R1, . . . , Rn, encoding each as a set of propositional constraints. If a SAT solver determines satisfiability then R is non-empty. Otherwise our solver uses unbounded model checking techniques to extract an interpolant from the bounded proof. This interpolant serves as an overapproximation of R. If the solver reaches a fixed-point with the constraints remaining unsatisfiable, it has proven R to be empty. Otherwise, it increases the unrolling depth and repeats. We compare revenant with other stateof-the-art string solvers. Evaluation suggests that it behaves better for constraints that express the intersection of sets of regular languages, a case of interest in the context of verification.

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“…Transformation (vi) implements a generalised version of the R-merge algorithm of [10] for reduction of non-deterministic automata. It was also described, as 'Collecting transitions' in [14].…”

Section: State Machine Slicingmentioning

confidence: 99%

Slicing Techniques for UML Models.

Lano¹,

Kolahdouz-Rahimi²

2011

JOT

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This paper defines techniques for the slicing of UML models, that is, for the restriction of models to those parts which specify the properties and behaviour of a subset of the elements within them. The purpose of this restriction is to produce a smaller model which permits more effective analysis and comprehension than the complete model, and also to form a step in factoring of a model. We consider class diagrams, single state machines, and communicating sets of state machines.

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Reducing the Size of NFAs by Using Equivalences and Preorders

Cited by 35 publications

References 21 publications

On the Inapproximability of Vertex Cover on k-Partite k-Uniform Hypergraphs

On the Inapproximability of Vertex Cover on k-Partite k-Uniform Hypergraphs

Unbounded Model-Checking with Interpolation for Regular Language Constraints

Slicing Techniques for UML Models.

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