Affiliations: School of Computer Science, Tel Aviv University, Tel
Aviv 69978, Israel
Abstract: Paradigms, in which continuous time is involved in cooperation with,
or instead of, discrete time appear now in different areas related to automata,
logic and interaction. Unfortunately, they are accompanied by a plethora of
definitions, terminology and notation, which is not free of ad-hoc and
ambiguous decisions. The overuse of definitions from scratch of intricate
notions without a previous, explicit core of basic generic notions engenders
further models and formalisms, and it is not clear where to stop. 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...". We undertake this challenge wrt some
automata-theoretic concepts and issues that appear in the literature on
continuous-time circuits and hybrid automata, by keeping to the following
guidelines: 1. Building on Basic Automata Theory. 2. Coherence with original or potential discrete-time paradigms, whose continuous-time analogs and/or mutants we would like to understand. 3. Functions, notably input/output behavior of devices, should not be ignored in favor of sets (languages) accepted by them. The paper outlines the approach which emerged in previous research [PRT, RT,
T3, T4, R] and in teaching experience [T0, T2]. As an illustration we offer a
precise explanation of the evasive relationship between hybrid automata,
constrained automata} and control circuits.
