NFA to DFA transformation for finite languages

Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1260)


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.


Regular Language Finite Automaton Deterministic Finite Automaton Nondeterministic Finite Automaton Finite Language 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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