Journal of Symbolic Computation
Theoretical Computer Science
Counting connected components of a semialgebraic set in subexponential time
Computational Complexity
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
UPPAAL—a tool suite for automatic verification of real-time systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First 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
The d/dt Tool for Verification of Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
An Improved Algorithm for Quantifier Elimination Over Real Closed Fields
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The theory of rectangular hybrid automata
The theory of rectangular hybrid automata
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Efficient solving of quantified inequality constraints over the real numbers
ACM Transactions on Computational Logic (TOCL)
Constraint Logic Programming using Eclipse
Constraint Logic Programming using Eclipse
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Taylor approximation for hybrid systems
Information and Computation
Hybrid Automata in Systems Biology: How Far Can We Go?
Electronic Notes in Theoretical Computer Science (ENTCS)
Algorithmic Algebraic Model Checking III: Approximate Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Progress on reachability analysis of hybrid systems using predicate abstraction
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Automated symbolic reachability analysis: with application to delta-notch signaling automata
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
| Hi-index | 5.23 |
Hybrid automata are a powerful formalism for the representation of systems evolving according to both discrete and continuous laws. Unfortunately, undecidability soon emerges when one tries to automatically verify hybrid automata properties. An important verification problem is the reachability one that demands to decide whether a set of points is reachable from a starting region. If we focus on semi-algebraic hybrid automata the reachability problem is semi-decidable. However, high computational costs have to be afforded to solve it. We analyse this problem by exploiting some existing tools and we show that even simple examples cannot be efficiently solved. It is necessary to introduce approximations to reduce the number of variables, since this is the main source of runtime requirements. We propose some standard approximation methods based on Taylor polynomials and ad hoc strategies. We implement our methods within the software SAHA-Tool and we show their effectiveness on two biological examples: the Repressilator and the Delta-Notch protein signaling.