The class NQP was proposed as the class of problems that are solvable by non-deterministic quantum Turing machines in polynomial time. In this paper, we introduce non-deterministic quantum finite automata in which the same non-determinism as in non-deterministic quantum Turing machines is applied. We compare non-deterministic quantum finite automata with the classical counterparts, and show that (unlike the case of classical finite automata) the class of languages recognizable by non-deterministic quantum finite automata properly contains the class of all regular languages.

This paper concerns a subclass of regular languages, called strictly regular languages, and studies the problem of identifying the class of strictly regular languages in the limit from positive data. We show that the class of strictly regular languages (SRLs) is polynomial time identifiable in the limit from positive data. That is, there is an algorithm that, for any strictly regular language L, identifies a finite automaton accepting L, called a strictly deterministic finite automaton (SDFA) in the limit from positive data, satisfying the property that the time for updating a conjecture is bounded by O(mN2), where m is the cardinality of the alphabet for L and N is the sum of lengths of all positive data provided. This is in contrast with the fact that the class of regular languages is not identifiable in the limit from positive data.