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ICALP
1994
Springer

On some Relations between Dynamical Systems and Transition Systems

9 years 6 months ago
On some Relations between Dynamical Systems and Transition Systems
Abstract. In this paper we de ne a precise notion of abstraction relation between continuous dynamical systems and discrete state-transition systems. Our main result states that every Turing Machine can be realized by a dynamical system with piecewise-constant derivatives in a 3-dimensional space and thus the reachability problem for such systems is undecidable for 3 dimensions. A decision procedure for 2-dimensional systems has been recently reported by Maler and Pnueli. On the other hand we show that some non-deterministic nite automata cannot be realized by any continuous dynamical system with less than 3 dimensions.
Eugene Asarin, Oded Maler
Added 09 Aug 2010
Updated 09 Aug 2010
Type Conference
Year 1994
Where ICALP
Authors Eugene Asarin, Oded Maler
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