Editing Hybrid system (section)

== Hybrid systems verification ==
There are approaches to automatically [[Formal verification|proving]] properties of hybrid systems (e.g., some of the tools mentioned below). Common techniques for proving safety of hybrid systems are computation of reachable sets, [[Abstraction model checking|abstraction refinement]], and [[barrier certificate]]s.

Most verification tasks are undecidable,<ref>Thomas A. Henzinger, Peter W. Kopke, Anuj Puri, and Pravin Varaiya: What's Decidable about Hybrid Automata, Journal of Computer and System Sciences, 1998</ref> making general verification [[algorithm]]s impossible. Instead, the tools are analyzed for their capabilities on benchmark problems. A possible theoretical characterization of this is algorithms that succeed with hybrid systems verification in all robust cases<ref>Martin Fränzle: Analysis of Hybrid Systems: An ounce of realism can save an infinity of states, Springer LNCS 1683</ref> implying that many problems for hybrid systems, while undecidable, are at least quasi-decidable.<ref>Stefan Ratschan: Safety verification of non-linear hybrid systems is quasi-decidable, Formal Methods in System Design, volume 44, pp. 71-90, 2014, {{doi|10.1007/s10703-013-0196-2}}</ref>