Piecewise and local threshold test ability of DFA

A. N. Trahtman

doi:10.1007/3-540-44669-9_33

Piecewise and local threshold test ability of DFA

A. N. Trahtman

Department of Mathematics

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

22 Scopus citations

Abstract

The necessary and sufficient conditions for an automaton to be locally threshold testable are found. We introduce the polynomial time algorithm to verify local threshold testability of the automaton of time complexity O(n⁵) and an algorithm of order O(n³) for the local threshold testability problem for syntactic semigroup of the automaton. We modify necessary and sufficient conditions for piecewise testability problem for deterministic finite automaton and improve the Stern algorithm to verify piecewise testability for the automaton. The time complexity of the algorithm is reduced from O(n⁵) to O(n²). An algorithm to verify piecewise testability for syntactic semigroup of the automaton of order O(n²) is presented as well. The algorithms have been implemented as a C/C⁺⁺package.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Rusins Freivalds
Publisher	Springer Verlag
Pages	347-358
Number of pages	12
ISBN (Print)	9783540446699
DOIs	https://doi.org/10.1007/3-540-44669-9_33
State	Published - 2001
Event	13th International Symposium on Fundamentals of Computation Theory, FCT 2001 - Riga, Latvia Duration: 22 Aug 2001 → 24 Aug 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2138
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Symposium on Fundamentals of Computation Theory, FCT 2001
Country/Territory	Latvia
City	Riga
Period	22/08/01 → 24/08/01

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

Keywords

Algorithm
Automaton
Locally testable
Locally threshold testable
Piecewise testable
Syntactic semigroup
Transition graph

Access to Document

10.1007/3-540-44669-9_33

Cite this

Trahtman, A. N. (2001). Piecewise and local threshold test ability of DFA. In R. Freivalds (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 347-358). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2138). Springer Verlag. https://doi.org/10.1007/3-540-44669-9_33

Trahtman, A. N. / Piecewise and local threshold test ability of DFA. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Rusins Freivalds. Springer Verlag, 2001. pp. 347-358 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The necessary and sufficient conditions for an automaton to be locally threshold testable are found. We introduce the polynomial time algorithm to verify local threshold testability of the automaton of time complexity O(n5) and an algorithm of order O(n3) for the local threshold testability problem for syntactic semigroup of the automaton. We modify necessary and sufficient conditions for piecewise testability problem for deterministic finite automaton and improve the Stern algorithm to verify piecewise testability for the automaton. The time complexity of the algorithm is reduced from O(n5) to O(n2). An algorithm to verify piecewise testability for syntactic semigroup of the automaton of order O(n2) is presented as well. The algorithms have been implemented as a C/C++package.",

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Trahtman, AN 2001, Piecewise and local threshold test ability of DFA. in R Freivalds (ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2138, Springer Verlag, pp. 347-358, 13th International Symposium on Fundamentals of Computation Theory, FCT 2001, Riga, Latvia, 22/08/01. https://doi.org/10.1007/3-540-44669-9_33

Piecewise and local threshold test ability of DFA. / Trahtman, A. N.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Rusins Freivalds. Springer Verlag, 2001. p. 347-358 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2138).

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

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Trahtman AN. Piecewise and local threshold test ability of DFA. In Freivalds R, editor, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2001. p. 347-358. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44669-9_33

Piecewise and local threshold test ability of DFA

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Keywords

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