Parametric real-time reasoning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Theoretical Computer Science
Achilles and the Tortoise climbing up the hyper-arithmetical hierarchy
Theoretical Computer Science - Special issue on real numbers and computers
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Achilles and the tortoise climbing up the arithmetical hierarchy
Journal of Computer and System Sciences - Fourteenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Integration Graphs: A Class of Decidable Hybrid Systems
Hybrid Systems
A Class of Rectangular Hybrid Systems with Computable Reach Set
Hybrid Systems IV
Decidability of Hybrid Systems with Rectangular Differential Inclusion
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Parameterized Complexity
Successive Abstractions of Hybrid Automata for Monotonic CTL Model Checking
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Decidable Compositions of O-Minimal Automata
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
A Uniform Approach to Three-Valued Semantics for μ-Calculus on Abstractions of Hybrid Automata
HVC '08 Proceedings of the 4th International Haifa Verification Conference on Hardware and Software: Verification and Testing
Property Driven Three-Valued Model Checking on Hybrid Automata
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Rational time-advance DEVS (RTA-DEVS)
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Proceedings of the 14th international conference on Hybrid systems: computation and control
Reachability problems on extended o-minimal hybrid automata
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Classes of Timed Automata and the Undecidability of Universality
Fundamenta Informaticae
Integer parameter synthesis for timed automata
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We define a new class of hybrid automata for which reachability is decidable--a proper superclass of the initialized rectangular hybrid automata--by taking parallel compositions of simple components. Attempting to generalize, we encounter timed automata with algebraic constants. We show that reachability is undecidable for these algebraic timed automata by simulating two-counter Minsky machines. Modifying the construction to apply to parametric timed automata, we reprove the undecidability of the emptiness problem, and then distinguish the dense and discrete-time cases with a new result. The algorithmic complexity-- both classical and parametric--of one-clock parametric timed automata is also examined. We finish with a table of computability-theoretic complexity results, including that the existence of a Zeno run is Σ11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.