A unified construction of the Glushkov, follow, and antimirov automata

Cyril Allauzen, Mehryar Mohri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A number of different techniques have been introduced in the last few decades to create ε-free automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods both for unweighted and weighted regular expressions. It describes simpler algorithms with time complexities at least as favorable as that of the best previously known techniques, and provides a concise proof of their correctness. Our algorithms are all based on two standard automata operations: epsilon-removal and minimization. This contrasts with the multitude of complicated and special-purpose techniques previously described in the literature, and makes it straightforward to generalize these algorithms to the weighted case. In particular, we extend the definition and construction of follow automata to the case of weighted regular expressions over a closed semiring and present the first algorithm to compute weighted Antimirov automata.

Original languageEnglish (US)
Title of host publicationMathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings
Pages110-121
Number of pages12
Volume4162 LNCS
StatePublished - 2006
Event31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006 - Stara Lesna, Slovakia
Duration: Aug 28 2006Sep 1 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4162 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006
CountrySlovakia
CityStara Lesna
Period8/28/069/1/06

Fingerprint

Automata
Regular Expressions
Weighted Automata
Proof of correctness
Semiring
Time Complexity
Closed
Generalise

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Allauzen, C., & Mohri, M. (2006). A unified construction of the Glushkov, follow, and antimirov automata. In Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings (Vol. 4162 LNCS, pp. 110-121). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4162 LNCS).

A unified construction of the Glushkov, follow, and antimirov automata. / Allauzen, Cyril; Mohri, Mehryar.

Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings. Vol. 4162 LNCS 2006. p. 110-121 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4162 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Allauzen, C & Mohri, M 2006, A unified construction of the Glushkov, follow, and antimirov automata. in Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings. vol. 4162 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4162 LNCS, pp. 110-121, 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006, Stara Lesna, Slovakia, 8/28/06.
Allauzen C, Mohri M. A unified construction of the Glushkov, follow, and antimirov automata. In Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings. Vol. 4162 LNCS. 2006. p. 110-121. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Allauzen, Cyril ; Mohri, Mehryar. / A unified construction of the Glushkov, follow, and antimirov automata. Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings. Vol. 4162 LNCS 2006. pp. 110-121 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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