Generalized PropertyDirected Reachability for Hybrid Systems Generalized propertydirected reachability (GPDR) belongs to the family of the modelchecking techniques called IC3PDR. It has been successfully applied to software verification; for example, it is the core of Spacer, a stateoftheart Hornclause solver bundled with Z3. However, it has yet to be applied to hybrid systems, which involve a continuous evolution of values over time. As the first step towards GPDRbased model checking for hybrid systems, this paper formalizes (textsc HGPDR), an adaptation of GPDR to hybrid systems, and proves its soundness. We also implemented a semiautomated proofofconcept verifier, which allows a user to provide hints to guide verification steps.

On Verifying Timed Hyperproperties We study the satisfiability and modelchecking problems for timed hyperproperties specified with HyperMTL, a timed extension of HyperLTL. Depending on whether interleaving of events in different traces is allowed, two possible semantics can be defined for timed hyperproperties: asynchronous and synchronous. While the satisfiability problem can be decided similarly to HyperLTL regardless of the choice of semantics, we show that the modelchecking problem, unless the specification is alternationfree, is undecidable even when very restricted timing constraints are allowed. On the positive side, we show that model checking HyperMTL with quantifier alternations is possible under certain conditions in the synchronous semantics, or when there is a fixed bound on the length of the time domain.