Behavior of G-Type Automata in a Matrix Game Against Automata with Linear Strategy

TLDR: Among the tremendous variety of environments (i.e., competitive situations) in which a G-type automaton can find itself, the following case is of special interest.

Abstract: Among the tremendous variety of environments (i.e., competitive situations) in which a G-type automaton can find itself (the definition of such an automaton and the basic notation was taken from Sragovich [1]), the following case is of special interest. Let M = ‖aij‖ be a numerical matrix with the dimension k × in, and let A be an automaton capable of m moves consisting of the selection of a number from a column of matrix M. In response to a move Yi, when i = 1, …,k, of a G-type automaton and of the j-th move of the A automaton, the former will be fed a number aij whereas the latter (which is defined by a certain rule) will be fed an element of its input alphabet. For the above G-type automaton, the matrix M and the automaton A are a switching environment.