Theoretical Computer Science
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
On the expressiveness and decidability of o-minimal hybrid systems
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Weighted O-Minimal Hybrid Systems Are More Decidable Than Weighted Timed Automata!
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Satisfiability of viability constraints for Pfaffian dynamics
PSI'06 Proceedings of the 6th international Andrei Ershov memorial conference on Perspectives of systems informatics
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In this paper we study a class of hybrid systems defined by Pfaffian maps. It is a sub-class of o-minimal hybrid systems which capture rich continuous dynamics and yet can be studied using finite bisimulations. The existence of finite bisimulations for o-minimal dynamical and hybrid systems has been shown by several authors (see e.g. [3,4,13]). The next natural question to investigate is how the sizes of such bisimulations can be bounded. The first step in this direction was done in [10] where a double exponential upper bound was shown for Pfaffian dynamical and hybrid systems. In the present paper we improve this bound to a single exponential upper bound. Moreover we show that this bound is tight in general, by exhibiting a parameterized class of systems on which the exponential bound is attained. The bounds provide a basis for designing efficient algorithms for computing bisimulations, solving reachability and motion planning problems.