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Circuits of finite memory retrospective operators

In this work we introduce a theory of circuits of finite memory retrospective operators to fully characterize the class of finite memory retrospective operators, expanding the theory developed by B. A. Trakhtenbrot and A. Rabinovich about automata over continuous time. A physical device, in which complex transformations are implemented, is usually an appropriate combination of elementary parts that interact as desired. These ideas conduct us to the concept of circuit which appears many times in literature. Our main contribution to this theory is the introduction of circuits of finite memory retrospective operators over signals, i.e., we choose a set of elementary finite memory operators and we study how to obtain all finite memory retrospective operators by constructing circuits with the elementary operators.