On the expressiveness and decidability of o-minimal hybrid systems

Authors:
Thomas Brihaye;Christian Michaux
Affiliations:
Universitè de Mons-Hainaut, Institut de Mathèmatique, 6, Avenue du Champ de Mars, 7000 Mons, Belgique;Universitè de Mons-Hainaut, Institut de Mathèmatique, 6, Avenue du Champ de Mars, 7000 Mons, Belgique
Venue:
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Year:
2005

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Abstract

This paper is driven by a general motto: bisimulate a hybrid system by a finite symbolic dynamical system. In the case of o-minimal hybrid systems, the continuous and discrete components can be decoupled, and hence, the problem reduces in building a finite symbolic dynamical system for the continuous dynamics of each location. We show that this can be done for a quite general class of hybrid systems defined on o-minimal structures. In particular, we recover the main result of a paper by G. Lafferriere, G.J. Pappas, and S. Sastry, on o-minimal hybrid systems. We also provide an analysis and extension of results on decidability and complexity of problems and constructions related to o-minimal hybrid systems.