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
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
&egr;-approximation of differential inclusions
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Deciding reachability for planar multi-polynomial systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
On some Relations between Dynamical Systems and Transition Systems
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
ICALP '97 Proceedings of the 24th 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
Hybrid Systems II
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Towards Computing Phase Portraits of Polygonal Differential Inclusions
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
The Power of QDDs (Extended Abstract)
SAS '97 Proceedings of the 4th International Symposium on Static Analysis
SPeeDI - A Verification Tool for Polygonal Hybrid Systems
CAV '02 Proceedings of the 14th 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
Symbolic Verification with Periodic Sets
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Computing invariance kernels of polygonal hybrid systems
Nordic Journal of Computing
Static analysis for state-space reduction of polygonal hybrid systems
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
A compositional algorithm for parallel model checking of polygonal hybrid systems
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Refining the undecidability frontier of hybrid automata
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools
Theoretical Computer Science
Reachability analysis of generalized polygonal hybrid systems
Proceedings of the 2008 ACM symposium on Applied computing
A Decidable Class of Planar Linear Hybrid Systems
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Relaxing Goodness Is Still Good
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Reachability analysis of GSPDIs: theory, optimization, and implementation
Proceedings of the 2010 ACM Symposium on Applied Computing
Interrupt Timed Automata: verification and expressiveness
Formal Methods in System Design
Reachability analysis of non-linear planar autonomous systems
FSEN'11 Proceedings of the 4th IPM international conference on Fundamentals of Software Engineering
Reachability analysis of nonlinear analog circuits through iterative reachable set reduction
Proceedings of the Conference on Design, Automation and Test in Europe
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In this work we are concerned with the formal verification of two-dimensional non-deterministic hybrid systems, namely polygonal differential inclusion systems (SPDIs). SPDIs are a class of non-deterministic systems that correspond to piecewise constant differential inclusions on the plane, for which we study the reachability problem. Our contribution is the development of an algorithm for solving exactly the reachability problem of SPDIs. We extend the geometric approach due to Maler and Pnueli [O. Maler, A. Pnueli. Reachability analysis of planar multi-linear systems. in: C. Courcoubetis (Ed.), CAV'93, in: LNCS, vol. 697, Springer-Verlag, 1993, pp. 194-209] to non-deterministic systems, based on the combination of three techniques: the representation of the two-dimensional continuous-time dynamics as a one-dimensional discrete-time system (using Poincare maps), the characterization of the set of qualitative behaviors of the latter as a finite set of types of signatures, and acceleration used to explore reachability according to each of these types.