Regular Expressions and NFAs Without ε-Transitions

Schnitger, Georg

doi:10.1007/11672142_35

Cited by 25 publications

(20 citation statements)

References 14 publications

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“…Note that if ∆ is considered to be fixed, the upper bound for the regular expression-to-NFA conversion can be improved [15,28]. Combining the results of Lemmas 5.1 and 5.2 with any graph reachability algorithm we have: Theorem 5.1.…”

Section: Proof First Assume That L(a)mentioning

confidence: 82%

Deciding determinism of caterpillar expressions

Salomaa

Yü

Zan

2009

Theoretical Computer Science

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a b s t r a c tCaterpillar expressions have been introduced by Brüggemann-Klein and Wood for applications in markup languages. Caterpillar expressions provide a convenient formalism for specifying the operation of tree-walking automata on unranked trees. Here we give a formal definition of determinism of caterpillar expressions that is based on the language of instruction sequences defined by the expression. We show that determinism of caterpillar expressions can be decided in polynomial time.

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Section: Proof First Assume That L(a)mentioning

confidence: 82%

Deciding determinism of caterpillar expressions

Salomaa

Yü

Zan

2009

Theoretical Computer Science

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“…Our algorithm does not assume a unit cost RAM model nor any restriction on the ratio between the size of the automaton t and the length of the sequences n. We further note that, in the case where the input is given in the form of a regular expression rather than an automaton, the complexity analysis of the algorithm can be expressed in terms of the length of the input regular expression. This is achieved based on recent algorithms which take as input a regular expression of length r and convert it into an e-free NFA with O(r) states and O(r log 2 r) transitions (Hromkoviěc et al, 2001;Schnitger, 2006;Geffert, 2003). This yields an O(n 2 r 2 log 2 r) time and O(n 2 r 2 ) space complexities for the algorithm of Chung et al We note that this was not observed by Arslan and Egecioglu (2005) and Chung et al (2007b).…”

Section: Resultsmentioning

confidence: 99%

Regular Language Constrained Sequence Alignment Revisited

Kucherov

Pinhas

Ziv-Ukelson

2011

Lecture Notes in Computer Science

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Imposing constraints in the form of a finite automaton or a regular expression is an effective way to incorporate additional a priori knowledge into sequence alignment procedures. With this motivation, the Regular Expression Constrained Sequence Alignment Problem was introduced, which proposed an O(n 2 t 4 ) time and O(n 2 t 2 ) space algorithm for solving it, where n is the length of the input strings and t is the number of states in the input non-deterministic automaton. A faster O(n 2 t 3 ) time algorithm for the same problem was subsequently proposed. In this article, we further speed up the algorithms for Regular Language Constrained Sequence Alignment by reducing their worst case time complexity bound to O(n 2 t 3 /log t). This is done by establishing an optimal bound on the size of Straight-Line Programs solving the maxima computation subproblem of the basic dynamic programming algorithm. We also study another solution based on a Steiner Tree computation. While it does not improve the worst case, our simulations show that both approaches are efficient in practice, especially when the input automata are dense.

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“…A third possibility is to obtain a (ǫ-free) NFA through the reverse regular expression, which can be done in polynomial time [24]. For example, the forward regular expression corresponds to c*(w, b)*s*(w, b)* and the reverse regular expression corresponds to (w, b)*s*(w, b)*c*.…”

Section: Modeling Backward Path Viabilitymentioning

confidence: 99%

State-based accelerations and bidirectional search for bi-objective multi-modal shortest paths

Artigues

Huguet

Guèye

et al. 2013

Transportation Research Part C: Emerging Technologies

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Taking into account the multi-modality of urban transportation networks for computing the itinerary of an individual passenger introduces a number of additional constraints such as mode restrictions and various objective functions. In this paper, constraints on modes are gathered under the concept of viable path, modeled by a non deterministic finite state automaton (NFA). The goal is to find the non-dominated viable shortest paths considering the minimization of the travel time and of the number of modal transfers. We show that the problem, initially considered by Lozano and Storchi [15], is a polynomially-solvable bi-objective variant of the mono-objective regular language-constrained shortest path problem [2,8].We propose several label setting algorithms for solving the problem: a topological label-setting algorithm improving on algorithms proposed by Pallottino and Scutellà [23] and Lozano and Storchi [15], a multi-label algorithm using buckets and its bidirectional variant, as well as dedicated goal oriented techniques. Furthermore, we propose a new NFA state-based dominance rule. The computational experiments, carried-out on a realistic urban network, show that the state-based dominance rule associated with bidirectional search yields significant average speed-ups. On an expanded graph comprising 1 859 350 nodes, we obtain on average 3.5 non-dominated shortest paths in less than 180 ms.keywords: bi-objective regular language-constrained shortest path problem, multimodal transportation, finite state automaton, label-setting algorithms, state-based dominance rule, bidirectional search, state-based estimated travel times.

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Regular Expressions and NFAs Without ε-Transitions

Cited by 25 publications

References 14 publications

Deciding determinism of caterpillar expressions

Deciding determinism of caterpillar expressions

Regular Language Constrained Sequence Alignment Revisited

State-based accelerations and bidirectional search for bi-objective multi-modal shortest paths

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