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
Timed automata and additive clock constraints
Information Processing Letters
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Widening the Boundary between Decidable and Undecidable Hybrid Systems
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
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
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
Algorithmic Algebraic Model Checking III: Approximate Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Algorithmic analysis of polygonal hybrid systems, part I: Reachability
Theoretical Computer Science
Reachability analysis of generalized polygonal hybrid systems
Proceedings of the 2008 ACM symposium on Applied computing
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
On the computational power of timed differentiable petri nets
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Low dimensional hybrid systems - decidable, undecidable, don't know
Information and Computation
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Reachability becomes undecidable in hybrid automata (HA) that can simulate a Turing (TM) or Minsky (MM) machine. Asarin and Schneider have shown that, between the decidable 2-dim Piecewise Constant Derivative (PCD) class and the undecidable 3-dim PCD class, there lies the “open” class 2-dim Hierarchical PCD (HPCD). This class was shown to be equivalent to the class of 1-dim Piecewise Affine Maps (PAM). In this paper, we first explore 2-dim HPCD's proximity to decidability, by showing that they are equivalent to 2-dim PCDs with translational resets, and to HPCDs without resets. A hierarchy of intermediates also equivalent to the HPCD class is presented, revealing semblance to timed and initialized rectangular automata. We then explore the proximity to the undecidability frontier. We show that 2-dim HPCDs with zeno executions or integer-checks can simulate the 2-counter MM. We conclude by retreating HPCDs as PAMs, to derive a simple over-approximating algorithm for reachability. This also defines a decidable subclass 1-dim Onto PAM (oPAM). The novel non-trivial transformation of 2-dim HPCDs into “almost decidable” systems, is likely to pave the way for approximate reachability algorithms, and the characterization of decidable subclasses. It is hoped that these ideas eventually coalesce into a complete understanding of the reachability problem for the class 2-dim HPCD (1-dim PAM).