The characteristic semigroup of an automaton interferes with the computational algorithm of generalized homomorphisms of automata; therefore, determining the complexity of the characteristic semigroup allows for the estimation of the computational complexity of generalized homomorphisms for other classes of automata. Within the scope of the mathematical model, the concept of a determined analog of an extension of automaton A associated with isomorphisms g, g,…, gq-1, where q is the degree of the extension, simulates a time-varying automaton under appropriate assumptions. A time-varying automaton is an adequate mathematical model for many technical and real-time computational processes. These automata simulate the operation of several automata using a single time-varying automaton. The direct sum of automata can be considered as a realization of – respectively – sequential calculations.COMPLEXITY OF THE CHARACTERISTIC SEMI-GROUP OF THE ASYNCHRONOUS AUTOMATONS DIRECT SUM OF THE STRONGLY
CONNECTED DETERMINED ANALOGS, THEIR EXTENSIONS ASSOCIATED
WITH ISOMORPHISMS
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 complexity of the computational 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 g, g, …gq-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 adequate mathematical model for the many technical and computational processes of the real time. The direct sum of automatons can be considered as the realization – sequence calculations accordingly. (…)
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Source: Logistyka Magazine