TY - JOUR

T1 - Reducing the time complexity of testing for local threshold testability

AU - Trahtman, A. N.

PY - 2004/11/29

Y1 - 2004/11/29

N2 - A locally threshold testable language L is a language with the property that for some non-negative integers k and l and for some word u from L, a word v belongs to L iff: (1) the prefixes [suffixes] of length k -1 of words u and v coincide, (2) the number of occurrences of every factor of length k in both words u and v are either the same or greater than I - 1. A deterministic finite automaton is called locally threshold testable if the automaton accepts a locally threshold testable language for some l and k. New necessary and sufficient conditions for a deterministic finite automaton to be locally threshold testable are found. On the basis of these conditions, we modify the algorithm to verify local threshold testability of the automaton, and to reduce the time complexity of the algorithm. The algorithm is implemented as a part of the C/C++ package TESTAS, http://www.cs.biu.ac.il/~trakht/Testas. html.

AB - A locally threshold testable language L is a language with the property that for some non-negative integers k and l and for some word u from L, a word v belongs to L iff: (1) the prefixes [suffixes] of length k -1 of words u and v coincide, (2) the number of occurrences of every factor of length k in both words u and v are either the same or greater than I - 1. A deterministic finite automaton is called locally threshold testable if the automaton accepts a locally threshold testable language for some l and k. New necessary and sufficient conditions for a deterministic finite automaton to be locally threshold testable are found. On the basis of these conditions, we modify the algorithm to verify local threshold testability of the automaton, and to reduce the time complexity of the algorithm. The algorithm is implemented as a part of the C/C++ package TESTAS, http://www.cs.biu.ac.il/~trakht/Testas. html.

KW - Algorithm

KW - Automaton

KW - Graph

KW - Threshold locally testable

UR - http://www.scopus.com/inward/record.url?scp=9544252205&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2004.07.011

DO - 10.1016/j.tcs.2004.07.011

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AN - SCOPUS:9544252205

SN - 0304-3975

VL - 328

SP - 151

EP - 160

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1-2

ER -