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.

• Type: Conference
• Year: 1994
• Where: ICALP
• Authors: Eugene Asarin, Oded Maler
• Keywords: Continuous Dynamical System, Discrete State-transition Systems, Dynamical System, ICALP 1994, Programming Languages