Algorithmic unsolvability of problem of recognition of recursive event representability by finite automata

An idea of recursive event formalizing the «event effectively given by a word description» is introduced. The problem of recognition of recursive events which are representable in a finite automaton is suggested and the theorem of its algorithmic unsolvability is proved. At the same time an idea of representation of a recursive function in a finite automaton is given and a recognizability criterion for representable recursive functions is given.
Some well-known ideas and facts are also explained because all these problems are discussed in «Avtomatika and Telemeckanika» for the first time.