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These models can also help to understand language acquisition, thinking and other mental activities. In this paper we consider finite automata with translucent letters. These models do not read their input strictly from left to right as traditional finite automata, but for each internal state of such a device, certain letters are translucent, that is, in this state the automaton cannot see them. We solve the parsing problem of these automata, both in the deterministic and in the nondeterministic cases. By introducing the permutation operator the class of regular languages is extended. It is shown that this extended class inside the class of languages that can be accepted by nondeterministic finite automata with translucent letters. 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