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Piecewise and Local Threshold Testability of DFA

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Fundamentals of Computation Theory (FCT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2138))

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Abstract

The necessary and sufficient conditions for an automaton to be locally threshold testable are found. We introduce the polynomial time algorithm to verify local threshold testability of the automaton of time complexity O(n 5) and an algorithm of order O(n 3) for the local threshold testability problem for syntactic semigroup of the automaton. We modify necessary and sufficient conditions for piecewise testability problem for deterministic finite automaton and improve the Stern algorithm to verify piecewise testability for the automaton. The time complexity of the algorithm is reduced from O(n 5) to O(n 2). An algorithm to verify piecewise testability for syntactic semigroup of the automaton of order O(n 2) is presented as well.

The algorithms have been implemented as a C/C ++ package.

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Author information

Authors and Affiliations

  1. Dep. of Math. and CS, Bar-Ilan University, 52900, Ramat Gan, Israel

    A. N. Trahtman

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  1. A. N. Trahtman
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Editors and Affiliations

  1. University of Latvia, Raiņa bulvaris 29, LV-1459, Riga, Latvia

    Rūsiņš Freivalds

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© 2001 Springer-Verlag Berlin Heidelberg

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Trahtman, A.N. (2001). Piecewise and Local Threshold Testability of DFA. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_33

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  • DOI: https://doi.org/10.1007/3-540-44669-9_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42487-1

  • Online ISBN: 978-3-540-44669-9

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