An algorithm to verify local threshold testability of deterministic finite automata

A. N. Trahtman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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 languageEnglish
Title of host publicationAutomata Implementation - 4th International Workshop on Implementing Automata, WIA 1999, Revised Papers
EditorsOliver Boldt, Helmut Jurgensen, Helmut Jurgensen
PublisherSpringer Verlag
Pages164-173
Number of pages10
ISBN (Print)9783540455264
StatePublished - 2001
Event4th International Workshop on Implementing Automata, WIA 1999 - Potsdam, Germany
Duration: 17 Jul 199919 Jul 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2214
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th International Workshop on Implementing Automata, WIA 1999
Country/TerritoryGermany
CityPotsdam
Period17/07/9919/07/99

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

Keywords

  • Algorithm
  • Deterministic finite automaton
  • Locally threshold testable
  • Semigroup

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