Advertisement

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)

Abstract

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).

Keywords

Automaton threshold locally testable graph algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. Beauquier, J.E. Pin, Factors of words, Lect. Notes in Comp. Sci., Springer, Berlin, 372(1989), 63–79.Google Scholar
  2. [2]
    J.A. Brzozowski, I. Simon, Characterizations of locally testable events, Discrete Math., 4(1973), 243–271.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Caron, LANGAGE: A Maple package for automaton characterization of regular languages, Springer, Lect. Notes in Comp. Sci., 1436(1998), 46–55.CrossRefGoogle Scholar
  4. [4]
    P. Caron, Families of locally testable languages, Theoret. Comput. Sci., 242(2000), 361–376.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    S. Kim, R. McNaughton, R. McCloskey, A polynomial time algorithm for the local testability problem of deterministic finite automata, IEEE Trans. Comput., 40(1991) N10, 1087–1093.CrossRefMathSciNetGoogle Scholar
  6. [6]
    S. Kim, R. McNaughton, Computing the order of a locally testable automaton, SIAM J. Comput., 23(1994), 1193–1215.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    R. McNaughton, S, Papert, Counter-free Automata M. I. T. Press. Mass., 1971.Google Scholar
  8. [8]
    J. Ruiz, S. Espana, P. Garcia, Locally threshold testable languages in strict sense: Application to the inference problem. Springer, Lect. Notes in Comp. Sci., 1433(1998), 150–161.MathSciNetCrossRefGoogle Scholar
  9. [9]
    R.E. Tarjan, Depth first search and linear graph algorithms, SIAM J. Comput., 1(1972), 146–160. J. of Comp. System Sci., 25(1982), 360–376.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    A.N. Trahtman, A polynomial time algorithm for local testability and its level. Int. J. of Algebra and Comp., vol. 9,1(1998), 31–39.CrossRefMathSciNetGoogle Scholar
  11. [11]
    A.N. Trahtman, Piecewise and local threshold testability of DFA. Fundam. of Comp. Theory, Riga, Springer, Lect. Notes in Comp. Sci., 2138 (2001), 347–358.MathSciNetCrossRefGoogle Scholar
  12. [12]
    A.N. Trahtman, A package TESTAS for checking some kinds of testability. Proc. of 7-th Int. Conf. on Implementation and Application of Automata. Tours, France, July 3–5, 2002, 223–227.Google Scholar
  13. [13]
    E. Vidal, F. Casacuberta, P. Garcia, Grammatical inference and automatic speech recognition. In Speech Recognition and Coding, Springer, 1995, 175–191.Google Scholar
  14. [14]
    Th. Wilke, Locally threshold testable languages of infinite words, Lect. Notes in Comp. Sci., Springer, Berlin, 665(1993), 63–79.Google Scholar
  15. [15]
    Th. Wilke, An algebraic theory for regular languages of finite and infinite words, Int. J. Alg. and Comput., 3(1993), 4, 447–489.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

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

Personalised recommendations