Parametric real-time reasoning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Theoretical Computer Science
Computability with low-dimensional dynamical systems
Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Universal computation and other capabilities of hybrid and continuous dynamical 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
Complexity and real computation
Complexity and real computation
Closed-form analytic maps in one and two dimensions can simulate universal Turing machines
Theoretical Computer Science - Special issue on real numbers and computers
Timed automata and additive clock constraints
Information Processing Letters
Communication and Concurrency
Expressiveness of Updatable Timed Automata
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
On some Relations between Dynamical Systems and Transition Systems
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Widening the Boundary between Decidable and Undecidable Hybrid Systems
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
Verfying Invariance Properties of Timed Systems with Duration Variables
ProCoS Proceedings of the Third International Symposium Organized Jointly with the Working Group Provably Correct Systems on Formal Techniques in Real-Time and Fault-Tolerant Systems
Integration Graphs: A Class of Decidable Hybrid Systems
Hybrid Systems
Towards a Geometric Theory of Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
On the Decidability of the Reachability Problem for Planar Differential Inclusions
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Reachability Analysis of Planar Multi-limear Systems
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Decidability of Hybrid Systems with Rectangular Differential Inclusion
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Verifying omega-Regular Properties for a Subclass of Linear Hybrid Systems
Proceedings of the 7th International Conference on Computer Aided Verification
Polyhedral Flows in Hybrid Automata
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Computation: finite and infinite machines
Computation: finite and infinite machines
Bisimulation relations for dynamical, control, and hybrid systems
Theoretical Computer Science
Algorithmic Algebraic Model Checking III: Approximate Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Computation in one-dimensional piecewise maps
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Refining the undecidability frontier of hybrid automata
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Reachability in one-dimensional controlled polynomial dynamical systems
PSI'11 Proceedings of the 8th international conference on Perspectives of System Informatics
Reachability analysis of nonlinear analog circuits through iterative reachable set reduction
Proceedings of the Conference on Design, Automation and Test in Europe
| Hi-index | 0.00 |
Even though many attempts have been made to define the boundary between decidable and undecidable hybrid systems, the affair is far from being resolved. More and more low dimensional systems are being shown to be undecidable with respect to reachability, and many open problems in between are being discovered. In this paper, we present various two-dimensional hybrid systems for which the reachability problem is undecidable. We show their undecidability by simulating Minsky machines. Their proximity to the decidability frontier is understood by inspecting the most parsimonious constraints necessary to make reachability over these automata decidable. We also show that for other two-dimensional systems, the reachability question remains unanswered, by proving that it is as hard as the reachability problem for piecewise affine maps on the real line, which is a well known open problem.