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 language | English |
---|---|
Title of host publication | Automata Implementation - 2nd International Workshop on Implementing Automata, WIA 1997, Revised Papers |
Editors | Derick Wood, Sheng Yu |
Publisher | Springer Verlag |
Pages | 198-212 |
Number of pages | 15 |
ISBN (Print) | 3540646949, 9783540646945 |
DOIs | |
State | Published - 1998 |
Event | 2nd International Workshop on Implementing Automata, WIA 1997 - London, Canada Duration: 18 Sep 1997 → 20 Sep 1997 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|
Volume | 1436 |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 2nd International Workshop on Implementing Automata, WIA 1997 |
---|---|
Country/Territory | Canada |
City | London |
Period | 18/09/97 → 20/09/97 |
Bibliographical note
Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1998.