The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Nonlinear control system design by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Complexity and real computation
Complexity and real computation
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
A Symbolic Approachto Modeling Cellular Behavior
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
Reachability Analysis of Delta-NotchLateral Inhibition Using Predicate Abstraction
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
A Symbolic Approachto Modeling Cellular Behavior
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
What Will Be Eventually True of Polynomial Hybrid Automata?
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Orthogonal Polyhedra: Representation and Computation
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Lateral Inhibition through Delta-Notch Signaling: A Piecewise Affine Hybrid Model
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Decidability of Hybrid Systems with Rectangular Differential Inclusion
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Bisimulation relations for dynamical, control, and hybrid systems
Theoretical Computer Science
Progress on reachability analysis of hybrid systems using predicate abstraction
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Model checking LTL over controllable linear systems is decidable
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Taylor approximation for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Taylor approximation for hybrid systems
Information and Computation
A Temporal Dynamic Logic for Verifying Hybrid System Invariants
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Hybrid Automata in Systems Biology: How Far Can We Go?
Electronic Notes in Theoretical Computer Science (ENTCS)
Discrete Semantics for Hybrid Automata
Discrete Event Dynamic Systems
European Train Control System: A Case Study in Formal Verification
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Algorithmic Algebraic Model Checking III: Approximate Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Hybrid automata, reachability, and Systems Biology
Theoretical Computer Science
Algebraic systems biology: theses and hypotheses
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Algorithmic algebraic model checking IV: characterization of metabolic networks
AB'07 Proceedings of the 2nd international conference on Algebraic biology
A dynamic algorithm for approximate flow computations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Logic and compositional verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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Motivated by applications to systems biology, and the emergence of semi-algebraic hybrid systems as a natural framework for modeling biochemical networks, we continue exploring the decidability problem for model-checking with TCTL (Timed Computation Tree Logic) over this broad class of semi-algebraic hybrid systems. Previously, we had introduced these models, demonstrated the close connection to the goals of systems biology. However, we had only developed the techniques for bounded reachability, arguing for the adequacy of such an approach in a majority of the biological applications. Here, we present a semi-decidable symbolic algebraic dense-time TCTL model checking algorithm, which satisfies two desirable properties: it can be derived automatically from the symbolic description, and it extends to and generalizes other versions of temporal logics. The main mathematical device at the core of this approach is Tarski-Collins’ real quantifier elimination employed at each fixpoint iteration, whose high complexity is the crux of its unfortunate limitation. Along with these results, we prove the undecidability of this problem in the more powerful “real” Turing machine formalism of Blum, Shub and Smale. We then demonstrate a preliminary version of our model-checker Tolque on the Delta-Notch example.