Precise estimation of the order of local testability of a deterministic finite automaton

A. N. Trahtman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

A locally testable language L is a language with the property that for some nonnegative integer k, called the order or the level of local testability, whether or not a word u 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. For given k the language is called k-testable. We give necessary and sufficient conditions for the language of an automaton to be k-testable in the terms of the length of paths of a related graph. Some estimations of the upper and of the lower bound of order of testability follow from these results. We improve the upper bound on the order of testability of locally testable deterministic finite automaton with n states to n2-n/2+1.This bound is the best possible. We give an answer on the following conjecture of Kim, McNaughton and McCloskey for deterministic finite locally testable automaton with n states: “Is the order of local testability no greater than Ω(n1,5) when the alphabet size is two?” Our answer is negative. In the case of size two the situation is the same as in general case: the order of local testability is Ω (n2).

Original languageEnglish
Title of host publicationAutomata Implementation - 2nd International Workshop on Implementing Automata, WIA 1997, Revised Papers
EditorsDerick Wood, Sheng Yu
PublisherSpringer Verlag
Pages198-212
Number of pages15
ISBN (Print)3540646949, 9783540646945
DOIs
StatePublished - 1998
Event2nd International Workshop on Implementing Automata, WIA 1997 - London, Canada
Duration: 18 Sep 199720 Sep 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1436
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd International Workshop on Implementing Automata, WIA 1997
Country/TerritoryCanada
CityLondon
Period18/09/9720/09/97

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.

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