The characteristic semigroup is a particularly important concept in automata theory; it carries significant information and determines the ability to process information. This has directly important practical consequences in the field of designing optimal logic circuits. The direct sum and direct product of automata can be considered as the implementation of sequential and parallel computations, respectively. A Finite State Machine (FSM, or digital automaton) is one of the models describing the behavior of control systems, in which the instantaneous operation of the system is naturally certain abstract models of digital circuits, that is, elements and circuits operating at discrete moments in time, where signals have a finite number of values. Automata theory, being a theoretical development of logic circuits, is an effective design tool, enabling the formal design of complex digital circuits using standard elementary circuits. (…)
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Source: Logistyka Magazine