A Family of NFAs Free of State Reductions

Merging states in finite automata is a main method of reducing the size of the representation of regular languages. The process has been extensively studied for deterministic finite automata, where the conditions for merging states can be efficiently computed. The matter is more complex in the case of non-deterministic finite automata, where merging states can be done in different ways, and the cost of detecting mergible states is high. In a recent paper the authors have studied one type of state mergibility and proven that one cannot have an arbitrarily large (in terms of number of states) nondeterministic automaton for a given language such that no states can be merged. In this paper we study a different type of state mergibility for non-deterministic automata, which is similar to the state mergibility in a deterministic finite automata. We prove that there are situations where state merging is impossible for arbitrary large equivalent non-deterministic automata.