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NFA to DFA transformation for finite languages

  • Kai Salomaa
  • Sheng Yu
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1260)

Abstract

We consider the number of states of a DFA that is equivalent to an n-state NFA accepting a finite language. We first give a detailed proof for the case where the finite languages are over a two-letter alphabet. It shows that O(2n/2) is the (worst-case) optimal upper-bound on the number of states of a DFA that is equivalent to an n-state NFA accepting a finite language. The main result of this paper is a generalization of the above result. We show that, for any n-state NFA accepting a finite language over an arbitrary k-letter alphabet, n, k>1, there is an equivalent DFA of \(O(k^{{n \mathord{\left/{\vphantom {n {(\log _2 k + 1)}}} \right.\kern-\nulldelimiterspace} {(\log _2 k + 1)}}} )\)states, and show that this bound is optimal in the worst case.

Keywords

Regular Language Finite Automaton Deterministic Finite Automaton Nondeterministic Finite Automaton Finite 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 1997

Authors and Affiliations

  • Kai Salomaa
    • 1
  • Sheng Yu
    • 1
  1. 1.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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