Generalized property-directed reachability (GPDR) belongs to the family of the model-checking techniques called IC3/PDR. It has been successfully applied to software verification; for example, it is the core of Spacer, a state-of-the-art Horn-clause 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 HGPDR, an adaptation of GPDR to hybrid systems, and proves its soundness. We also implemented a semi-automated proof-of-concept verifier, which allows a user to provide hints to guide verification steps.
A new model of filamentary matter fields and voids is proposed. This is a gravitational version of the MIT bag model of hadrons (see a review of DeTar and Donoghue 1983). Bekenstein and Milgrom(1984) have first proposed a gravitational bag model. Their bag is closed but our bag, called a channel, is open.We start from the action in the weak limt of gravity oo
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