Mergible states in large NFA

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.