A course in computational algebraic number theory
A course in computational algebraic number theory
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Decidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Minimal Solutions of Linear Diophantine Systems: Bounds and Algorithms
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Composing semi-algebraic O-minimal automata
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
AB'07 Proceedings of the 2nd international conference on Algebraic biology
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We identify a new class of decidable hybrid automata: namely, parallel compositions of semi-algebraic o-minimal automata. The class we consider is fundamental to hierarchical modeling in many exemplar systems, both natural and engineered. Unfortunately, parallel composition, which is an atomic operator in such constructions, does not preserve the decidability of reachability. Luckily, this paper is able to show that when one focuses on the composition of semi-algebraic o-minimal automata, it is possible to translate the decidability problem into a satisfiability problem over formulæinvolving both real and integer variables. While in the general case such formulæ would be undecidable, the particular format of the formulæ obtained in our translation allows combining decidability results stemming from both algebraic number theory and first-order logic over (茂戮驴, 0, 1, + , *,