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Библиогр.: 10 назв.

The paper continues an investigation of the cryptanalytical invertibility concept of finite automata with a finite delay introduced by the author in his previous papers where he also gave a constructive set theory test for an automaton A to be cryptana- lytically invertible, that is, to have a recovering function f which allows to calculate a prefix of a length m in an input sequence of the automaton A by using its output sequence of a length m + т and some additional information about A known to cryptanalysts, defining a type of its invertibility and of its recovering functon. Here, we expound a test for that of another kind, namely some logical necessary and sufficient conditions for an automaton A to have or not a recovering function f of a certain type. Results related to specific types of automata invertibility (invertibility tests, inversion algorithms, synthesis of inverse automata and others) are subjects of further researching and publications.