Pattern languages with and without erasing

Jiang, Tao; Kinber, Efim; Salomaa, Arto; Salomaa, Kai; Yü, Sheng

doi:10.1080/00207169408804252

Cited by 50 publications

(55 citation statements)

References 4 publications

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“…We define the pattern language of a terminal-free pattern α by L Σ (α) := {σ(α) | σ : X * → Σ * is a substitution}. Note, that these languages, technically, are terminal-free E-pattern languages (see Jiang et al [9]). Since in our work the dependency on the alphabet Σ is negligible, we mostly denote pattern languages by L(α).…”

Section: Basic Definitionsmentioning

confidence: 99%

“…If, for some pattern α and some x i ∈ var(α), varpos i (α) := {1, 3, 5, 9, 14}, then the sequences ((5, 1), (14,3), (1,3), (9, 3)), ((1, 3), (3,5), (5,9), (9,14)) and ( (5, 1), (5,3), (5,9), (5,14)) are some of the possible matching orders for x i in α, whereas the sequences ((1, 3), (9, 1), (3,9), (5, 14)) and ( (1, 3), (3,5), (5,9), (9, 1)) do not satisfy the conditions to be matching orders for x i in α.…”

Section: Janus Automata For Pattern Languagesmentioning

confidence: 99%

“…Thus, it is not surprising that the membership problem for pattern languages is also known to be NP-complete (see Angluin [8] and Jiang et al [9]). Furthermore, Ibarra et al [10] point out that the membership problem for pattern languages is closely related to the solvability problem for certain Diophantine equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Polynomial Time Match Test for Large Classes of Extended Regular Expressions

Reidenbach

Schmid

2011

Implementation and Application of Automata

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In the present paper, we study the match test for extended regular expressions. We approach this NP-complete problem by introducing a novel variant of two-way multihead automata, which reveals that the complexity of the match test is determined by a hidden combinatorial property of extended regular expressions, and it shows that a restriction of the corresponding parameter leads to rich classes with a polynomial time match test. For presentational reasons, we use the concept of pattern languages in order to specify extended regular expressions. While this decision, formally, slightly narrows the scope of our results, an extension of our concepts and results to more general notions of extended regular expressions is straightforward.

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Section: Basic Definitionsmentioning

confidence: 99%

Section: Janus Automata For Pattern Languagesmentioning

confidence: 99%

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A Polynomial Time Match Test for Large Classes of Extended Regular Expressions

Reidenbach

Schmid

2011

Implementation and Application of Automata

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“…The relevance of Theorem 6 for the research on the equivalence problem for E-pattern languages follows from a result by Jiang et al [8] which says that, for alphabets with at least three letters, two patterns need to be similar if they generate the same E-pattern language:…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Jiang et al [8]), word equations (cf. Mateescu, Salomaa [12], Karhumäki et al [10]) and equality sets (and, thus, the Post Correspondence Problem, cf.…”

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confidence: 99%

Bad News on Decision Problems for Patterns

Freydenberger

Reidenbach

2008

Developments in Language Theory

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Abstract. We study the inclusion problem for pattern languages, which is shown to be undecidable by Jiang et al. (J. Comput. System Sci. 50, 1995). More precisely, Jiang et al. demonstrate that there is no effective procedure deciding the inclusion for the class of all pattern languages over all alphabets. Most applications of pattern languages, however, consider classes over fixed alphabets, and therefore it is practically more relevant to ask for the existence of alphabet-specific decision procedures. Our first main result states that, for all but very particular cases, this version of the inclusion problem is also undecidable. The second main part of our paper disproves the prevalent conjecture on the inclusion of so-called similar E-pattern languages, and it explains the devastating consequences of this result for the intensive previous research on the most prominent open decision problem for pattern languages, namely the equivalence problem for general E-pattern languages.

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Decision Problems for Patterns

Jiang

Salomaa

et al. 1995

Journal of Computer and System Sciences

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We settle an open problem, the inclusion problem for pattern languages 1, 2]. This is the rst known case where inclusion is undecidable for generative devices having a trivially decidable equivalence problem. The study of patterns goes back to the seminal work of Thue 16] and is important also, for instance, in recent work concerning inductive inference and learning. Our results concern both erasing and nonerasing patterns.

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Pattern languages with and without erasing

Cited by 50 publications

References 4 publications

A Polynomial Time Match Test for Large Classes of Extended Regular Expressions

A Polynomial Time Match Test for Large Classes of Extended Regular Expressions

Bad News on Decision Problems for Patterns

Decision Problems for Patterns

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