Abstract
In this paper we answer an open question about the exact bound on the maximal number of non-mergible states in nondeterministic finite automaton (NFA). It is shown that the maximal possible number of non-mergible states in a NFA that accepts a given regular language L is not greater than 2n – 1, where n is the number of states in the minimal deterministic finite automaton that accepts L. Next we show that the bound is reachable by constructing a NFA that have exactly 2n – 1 non-mergible states. As a generalization of this result we show that the number of states in a NFA that does not contain a subset of k mergible states, where k > 1, is bounded by (k – 1)(2n – 1) and the bound is reachable.
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Grunsky, I., Kurganskyy, O., Potapov, I. (2006). On a Maximal NFA Without Mergible States. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_22
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DOI: https://doi.org/10.1007/11753728_22
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Print ISBN: 978-3-540-34166-6
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