Abstract
The principal objective of this paper is to lift basic concepts of the classical automata theory from discrete to continuous (real) time. It is argued that the set of finite memory retrospective functions is the set of functions realized by finite state devices. We show that the finite memory retrospective functions are speed-independent, i.e., they are invariant under ‘stretchings’ of the time axis. Therefore, such functions cannot deal with metrical aspects of the reals. We classify and analyze phenomena which appear at continuous time and are invisible at discrete time.
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