On a maximal NFA without mergible states

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 2 n - 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 2 n - 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)(2 n - 1) and the bound is reachable. © Springer-Verlag Berlin Heidelberg 2006.