Lower Bound for the Power of an Automaton State Code

A lower bound is found for the number $M$ of states of an automaton stable under races and errors of any $t$ or fewer of the total number $n$ of its internal elements. The bound is derived by random encoding of the states of the automaton with code words of length $n$. A set of code words that guarantees the indicated property for an automaton is called an automaton state code. The problem is solved in the general case of $q$-position internal elements, and in this connection two race models are proposed. An upper bound is found for the correcting capacity $t$ of an automaton state code, such that the power $M$ of the code preserves exponential growth. In particular, for $q=2$ the latter is true as long as $t<n/16$.