B.A. Trakhtenbrot, Tel-Aviv University,
The development of paradigms, in which continuous time is involved in cooperation with, or instead of, discrete time, is dominated by a plethora of definitions, terminology and notation. Hence (quoting J.Hartmanis), the challenge ``to isolate the right concepts, to formulate the right models, and to discard many others, that do not capture the reality we want to understand...".
Building on mainstream, basic Automata Theory, we undertake this challenge wrt some aspects of the paradigms mentioned in the title.
Note, that some phenomena are handled in the literature alone for continuous time, merely because their natural discrete-time counterparts were not considered previously. In such cases we discuss those discrete-time issues, whose continuous-time analogs and/or mutants we would like to understand.