The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA ’98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language using a Non-deterministic Finite Automata (NFA) may significantly reduce the number of required states. The combined power of the succinctness of the representation of finite languages using both cover languages and non-determinism has been suggested, but never systematically studied. In the present paper, for non-deterministic finite cover automata (NFCA) and l-non-deterministic finite cover automaton (l-NFCA), we show that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets. Moreover, we show how we can adapt the methods used to reduce, or minimize the size of NFAs/DFCAs/l-DFCAs, for simplifying NFCAs/l-NFCAs.

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