The study constructs basis of finite automata associated with the deductibility of words in the Post normal calculus. The researcher determines operators implemented by logical networks over this basis. They are computable in Moore’s vending machines, but their class is recursively unsolvable. When introducing restrictions on the complexity of the network, the set of relevant operators becomes recursive.

Key word: finite automata, logical networks, deductibility of words, recursively unsolvable sets.