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.
This research is supported by the Natural Sciences and Engineering Research Council of Canada grants OGP0041630.
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© 1997 Springer-Verlag Berlin Heidelberg
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Salomaa, K., Yu, S. (1997). NFA to DFA transformation for finite languages. In: Raymond, D., Wood, D., Yu, S. (eds) Automata Implementation. WIA 1996. Lecture Notes in Computer Science, vol 1260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63174-7_12
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DOI: https://doi.org/10.1007/3-540-63174-7_12
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