Złożoność półgrupy charakterystycznej sumy prostej automatów synchronicznych silnie spójnych i ustalonych analogów ich rozszerzeń dla każdego słowa z języka n-ary sumation+= (sigma 0 union sigma 1)+

The characteristic semi-group of the automaton interferes in the computational algorithm of the generalized homeomorphisms of the automatons. Then determination the complexity of the characteristic semi-group enables to estimate the computational complexity of the generalized homeomorphisms for the other classes of automatons. In the range of the mathematical model the conception of the determined analog of the extension of the automaton A associated with the isomorphisms g0' g1,..., g q-1 where q is the grade of the extensions, with the suitable assumptions it simulates the automaton variable in time. The variable automaton in time is the adeąuate mathematical model for the many technical and computational processes of the real time. These automatons simulate the work of several automatonsza by means of one automaton variable in time. The direct sum of automatons can be considered as the realization - sequence calculations accordingly.