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 an 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 real-time technical and computational processes. These automata simulate the operation of several automata using a single time-varying automaton. The direct product of automata can be considered as a realization of parallel computations accordingly.COMPLEXITY OF THE CHARACTERISTIC SEMI-GROUP OF THE ASYNCHRONOUS AUTOMATONS DIRECT PRODUCT OF THE STRONGLY
CONNECTED DETERMINED ANALOGS, 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 product of automatons can be considered as the realization parallel calculations accordingly. (…)
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Source: Logistyka Magazine