Type meeting problem for automata in labyrinths

The paper studies one special type of interaction of automata collectives in labyrinths. The following problem is considered for a given class of labyrinths: for which pairs of collective types there is a collective of the first type and a collective of the second type that will certainly meet, if at the starting moment they are placed in any two vertices of any labyrinth of the given class. We call this the problem of the ‘type meeting’ for automata in the given class of labyrinths. Here the problem is completely solved both for the case of the class of all finite plane mosaic labyrinths and for the case of the class of all finite plane rectangular labyrinths. The problem remains unsolved so far for the case of all (finite and non finite) mosaic labyrinths for some pairs of collective types, whereas for the case of the class of all plane rectangular labyrinths, the problem of type meeting is completely unexplored.