An algorithm to verify local threshold testability of deterministic finite automata

A. N. Trahtman

An algorithm to verify local threshold testability of deterministic finite automata

A. N. Trahtman

Department of Mathematics

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

5 Scopus citations

Abstract

A locally threshold testable language L is a language with the property that for some nonnegative integers k and l, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k-1 and (2) the set of intermediate substrings of length k of the word u where the sets of substrings occurring at least j times are the same, for j ≤ l. For given k and l the language is called l-threshold k-testable. A finite deterministic automaton is called l-threshold k-testable if the automaton accepts a l-threshold k-testable language. In this paper, the necessary and sufficient conditions for an automaton to be locally threshold testable are found. We introduce the first polynomial time algorithm to verify local threshold testability of the automaton based on this characterization. New version of polynomial time algorithm to verify the local testability will be presented too.

Original language	English
Title of host publication	Automata Implementation - 4th International Workshop on Implementing Automata, WIA 1999, Revised Papers
Editors	Oliver Boldt, Helmut Jurgensen, Helmut Jurgensen
Publisher	Springer Verlag
Pages	164-173
Number of pages	10
ISBN (Print)	9783540455264
State	Published - 2001
Event	4th International Workshop on Implementing Automata, WIA 1999 - Potsdam, Germany Duration: 17 Jul 1999 → 19 Jul 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2214
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Workshop on Implementing Automata, WIA 1999
Country/Territory	Germany
City	Potsdam
Period	17/07/99 → 19/07/99

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

Keywords

Algorithm
Deterministic finite automaton
Locally threshold testable
Semigroup

Cite this

Trahtman, A. N. (2001). An algorithm to verify local threshold testability of deterministic finite automata. In O. Boldt, H. Jurgensen, & H. Jurgensen (Eds.), Automata Implementation - 4th International Workshop on Implementing Automata, WIA 1999, Revised Papers (pp. 164-173). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2214). Springer Verlag.

Trahtman, A. N. / An algorithm to verify local threshold testability of deterministic finite automata. Automata Implementation - 4th International Workshop on Implementing Automata, WIA 1999, Revised Papers. editor / Oliver Boldt ; Helmut Jurgensen ; Helmut Jurgensen. Springer Verlag, 2001. pp. 164-173 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Trahtman, AN 2001, An algorithm to verify local threshold testability of deterministic finite automata. in O Boldt, H Jurgensen & H Jurgensen (eds), Automata Implementation - 4th International Workshop on Implementing Automata, WIA 1999, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2214, Springer Verlag, pp. 164-173, 4th International Workshop on Implementing Automata, WIA 1999, Potsdam, Germany, 17/07/99.

An algorithm to verify local threshold testability of deterministic finite automata. / Trahtman, A. N.
Automata Implementation - 4th International Workshop on Implementing Automata, WIA 1999, Revised Papers. ed. / Oliver Boldt; Helmut Jurgensen; Helmut Jurgensen. Springer Verlag, 2001. p. 164-173 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2214).

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

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Trahtman AN. An algorithm to verify local threshold testability of deterministic finite automata. In Boldt O, Jurgensen H, Jurgensen H, editors, Automata Implementation - 4th International Workshop on Implementing Automata, WIA 1999, Revised Papers. Springer Verlag. 2001. p. 164-173. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

An algorithm to verify local threshold testability of deterministic finite automata

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