Generalized one-unambiguity

Pascal Caron; Yo Sub Han; Ludovic Mignot

doi:10.1007/978-3-642-22321-1_12

Generalized one-unambiguity

Pascal Caron, Yo Sub Han, Ludovic Mignot

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

10 Citations (Scopus)

Abstract

Brüggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E)∈=∈L and the position automaton of E is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (n∈+∈2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.

Original language	English
Title of host publication	Developments in Language Theory - 15th International Conference, DLT 2011, Proceedings
Pages	129-140
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-22321-1_12
Publication status	Published - 2011
Event	15th International Conference on Developments in Language Theory, DLT 2011 - Milan, Italy Duration: 2011 Jul 19 → 2011 Jul 22

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6795 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	15th International Conference on Developments in Language Theory, DLT 2011
Country	Italy
City	Milan
Period	11/7/19 → 11/7/22

Bibliographical note

Funding Information:
Han was supported by the Basic Science Research Program through NRF funded by MEST (2010-0009168).

Funding Information:
★ Han was supported by the Basic Science Research Program through NRF funded by MEST (2010-0009168).

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-642-22321-1_12

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Caron, P., Han, Y. S., & Mignot, L. (2011). Generalized one-unambiguity. In Developments in Language Theory - 15th International Conference, DLT 2011, Proceedings (pp. 129-140). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6795 LNCS). https://doi.org/10.1007/978-3-642-22321-1_12

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title = "Generalized one-unambiguity",

abstract = "Br{\"u}ggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E)∈=∈L and the position automaton of E is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (n∈+∈2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.",

author = "Pascal Caron and Han, {Yo Sub} and Ludovic Mignot",

note = "Funding Information: Han was supported by the Basic Science Research Program through NRF funded by MEST (2010-0009168). Funding Information: ★ Han was supported by the Basic Science Research Program through NRF funded by MEST (2010-0009168).; 15th International Conference on Developments in Language Theory, DLT 2011 ; Conference date: 19-07-2011 Through 22-07-2011",

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Caron, P, Han, YS & Mignot, L 2011, Generalized one-unambiguity. in Developments in Language Theory - 15th International Conference, DLT 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6795 LNCS, pp. 129-140, 15th International Conference on Developments in Language Theory, DLT 2011, Milan, Italy, 11/7/19. https://doi.org/10.1007/978-3-642-22321-1_12

Generalized one-unambiguity. / Caron, Pascal; Han, Yo Sub; Mignot, Ludovic.

Developments in Language Theory - 15th International Conference, DLT 2011, Proceedings. 2011. p. 129-140 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6795 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Han, Yo Sub

AU - Mignot, Ludovic

N1 - Funding Information: Han was supported by the Basic Science Research Program through NRF funded by MEST (2010-0009168). Funding Information: ★ Han was supported by the Basic Science Research Program through NRF funded by MEST (2010-0009168).

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N2 - Brüggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E)∈=∈L and the position automaton of E is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (n∈+∈2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.

AB - Brüggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E)∈=∈L and the position automaton of E is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (n∈+∈2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.

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Generalized one-unambiguity

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