Distinguishability of vertices of automaton labyrinths by finite automata

We study the behavior of finite automata in automaton labyrinths. We introduce the concept of distinguishability by an automaton of vertices of labyrinths that is useful in various problems related to the recognition by an automaton of unknown characteristics of labyrinths. We obtain sharp estimates for the least time for an automaton to distinguish two distinguishable vertices of one or two automaton labyrinths.