Hilbert's tenth problem
Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Logic: from foundations to applications
Complexity and real computation
Complexity and real computation
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Information and Computation
Hybrid Automata with Finite Bisimulatioins
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
CAV '90 Proceedings of the 2nd International Workshop on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Language-based abstraction refinement for hybrid system verification
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
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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.