TY - JOUR

T1 - Algorithms finding the order of local testability of deterministic finite automaton and estimations of the order

AU - Trahtman, A. N.

PY - 2000/3/17

Y1 - 2000/3/17

N2 - 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 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. For given k the language is called k-testable. A finite deterministic automaton is called k-testable if the automaton accepts a k-testable language. In this paper, algorithms to verify 2-testability of order O(n3), 3-testability of order O(n4) and j-testability for j > 3 of order O(nj+1) are presented. An O(nn+2) time algorithm of finding the precise order of local testability is described. The time complexity of the algorithms improves on the previously known algorithms. We give necessary and sufficient conditions for an automaton to be k-testable in terms of the length of paths of related graphs. Some estimates of the upper and of the lower bound on the order of local testability follow.

AB - 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 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. For given k the language is called k-testable. A finite deterministic automaton is called k-testable if the automaton accepts a k-testable language. In this paper, algorithms to verify 2-testability of order O(n3), 3-testability of order O(n4) and j-testability for j > 3 of order O(nj+1) are presented. An O(nn+2) time algorithm of finding the precise order of local testability is described. The time complexity of the algorithms improves on the previously known algorithms. We give necessary and sufficient conditions for an automaton to be k-testable in terms of the length of paths of related graphs. Some estimates of the upper and of the lower bound on the order of local testability follow.

KW - Algorithm

KW - Finite automaton

KW - Locally testable

KW - Order of local testability

KW - Semigroup

UR - http://www.scopus.com/inward/record.url?scp=0347338089&partnerID=8YFLogxK

U2 - 10.1016/S0304-3975(99)00191-7

DO - 10.1016/S0304-3975(99)00191-7

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AN - SCOPUS:0347338089

SN - 0304-3975

VL - 235

SP - 183

EP - 204

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1

ER -