Quite often, trivial problems stated for deterministic finite automata (DFA) are surprisingly difficult for the non-deterministic case (NFA). In any non-minimal DFA for a given regular language, we can find two equivalent states which can be "merged" without changing the accepted language. This is not the case for NFA, where we can have non-minimal automata with no "mergible" states. In this paper, we prove a very basic result for NFA, that for a given regular language, any NFA of size greater than a computable constant must contain mergible states. Even more, we parameterized this constant in order to guarantee groups of an arbitrary number of mergible states. © 2004 Elsevier B.V. All rights reserved.
Câmpeanu, C., Sântean, N., & Yu, S. (2005). Mergible states in large NFA. Theoretical Computer Science, 330(1), 23–34. https://doi.org/10.1016/j.tcs.2004.09.008