Solution of the generalized minimization problem for two-tape automata with one fixed tape

A solution of the generalized minimization problem for two-tape automata with one fixed tape always filled with a fixed symbol, is provided. The problem was formulated to find an automaton with a minimal number of states in its equivalence and to describe a procedure whereby the automaton found is used to construct any minimal automaton in the same equivalence class. For every automaton, an auxiliary finite automaton can be constructed by supplying the arcs issuing from each state with an additional label of that state. Two-typwe automata are called strongly equivalent if their auxiliary finite automations are equivalent in the usual sense. It was established that the set of automata contains equivalence classes with an infinite number of deadlock automata.