Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Model-checking in dense real-time
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
IEEE Spectrum
Linear phase-portrait approximations for nonlinear hybrid systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
IEEE Transactions on Software Engineering - Special issue on formal methods in software practice
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Automatic Symbolic Verification of Embedded Systems
IEEE Transactions on Software Engineering
Automated Analysis of an Audio Control Protocol
Proceedings of the 7th International Conference on Computer Aided Verification
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
Dynamic distributed intrusion detection for secure multi-robot systems
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
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A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete updates with differential constraints for capturing continuous flows. Formal verification of hybrid automata relies on symbolic fixpoint computation procedures that manipulate sets of states. These procedures can be implemented using boolean combinations of linear constraints over system variables, equivalently, using polyhedra, for the subclass of linear hybrid automata. In a linear hybrid automaton, the flow at each control mode is given by a rate polytope that constrains the allowed values of the first derivatives. The key property of such a flow is that, given a state-set described by a polyhedron, the set of states that can be reached as time elapses, is also a polyhedron. We call such a flow a polyhedral flow. In this paper, we study if we can generalize the syntax of linear hybrid automata for describing flows without sacrificing the polyhedral property. In particular, we consider flows described by origin-dependent rate polytopes, in which the allowed rates depend, not only on the current control mode, but also on the specific state at which the mode was entered. We identify necessary and sufficient conditions for a class of flows described by origin-dependent rate polytopes to be polyhedral. We also propose and study additional classes of flows: strongly polyhedral flows, in which the set of states that can be reached up to a given time starting from a polyhedron is guaranteed to be a polyhedron, and polyhedrally sliced flows, in which the set of states that can be reached at a given time starting from a polyhedron is guaranteed to be a polyhedron. Finally, we discuss an application of the above classes of flows to approximate exponential behaviours.