3 research outputs found
Sharper and Simpler Nonlinear Interpolants for Program Verification
Interpolation of jointly infeasible predicates plays important roles in
various program verification techniques such as invariant synthesis and CEGAR.
Intrigued by the recent result by Dai et al.\ that combines real algebraic
geometry and SDP optimization in synthesis of polynomial interpolants, the
current paper contributes its enhancement that yields sharper and simpler
interpolants. The enhancement is made possible by: theoretical observations in
real algebraic geometry; and our continued fraction-based algorithm that rounds
off (potentially erroneous) numerical solutions of SDP solvers. Experiment
results support our tool's effectiveness; we also demonstrate the benefit of
sharp and simple interpolants in program verification examples
Generalized Property-Directed Reachability for Hybrid Systems
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 GPDR- based 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.Comment: To appear in VMCAI 202