Reducing the Time Complexity of Testing for Local Threshold Testability

  • Avraham Trakhtman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2759)


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 suf- fix 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 threshold locally testable if the automaton accepts a l-threshold ktestable 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 reduce the time complexity of the algorithm. The algorithm is implemented as a part of C/C ++ package TESTAS (testability of automata and semigroups).


Automaton threshold locally testable graph algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Avraham Trakhtman
    • 1
  1. 1.Dep. of Math. and CSBar-Ilan UniversityRamat GanIsrael

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