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An upper bound on the order of locally testable deterministic finite automata

  • Sam Kim
  • Robert McNaughton
  • Robert McCloskey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 401)

Abstract

A locally testable language is a language with the property that for some nonnegative integer k, called the order of locality, whether or not a word w is in the language depends on (1) the prefix and suffix of w of length k, and (2) the set of intermediate substrings of w of length k + 1, without regard to the order in which these substrings occur. The local testability problem is, given a deterministic finite automaton, to decide whether it accepts a locally testable language or not. Recently, we introduced the first polynomial time algorithm for the local testability problem based on a simple characterization of locally testable deterministic automata. This paper investigates the upper bound on the order of locally testable automata. It shows that the order of a locally testable deterministic automaton is at most n4 + 1, where n is the number of states of the automaton.

Keywords

Polynomial Time Algorithm Finite Automaton Transition Graph Closed Path Testable Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Sam Kim
    • 1
  • Robert McNaughton
    • 1
  • Robert McCloskey
    • 1
  1. 1.Computer Science DepartmentRensselaer Polytechnic InstituteTroy

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