Set Containment Characterization
Journal of Global Optimization
Characterizing Set Containments Involving Infinite Convex Constraints and Reverse-Convex Constraints
SIAM Journal on Optimization
Convex Optimization
OPERA: optimization with ellipsoidal uncertainty for robust analog IC design
Proceedings of the 42nd annual Design Automation Conference
Robust analog/RF circuit design with projection-based posynomial modeling
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Efficient solving of quantified inequality constraints over the real numbers
ACM Transactions on Computational Logic (TOCL)
HySAT: An efficient proof engine for bounded model checking of hybrid systems
Formal Methods in System Design
Tool-support for the analysis of hybrid systems and models
Proceedings of the conference on Design, automation and test in Europe
Bounded model checking of analog and mixed-signal circuits using an SMT solver
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Symbolic reachability analysis of lazy linear hybrid automata
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
Safety verification of conflict resolution manoeuvres
IEEE Transactions on Intelligent Transportation Systems
Optimal design of a CMOS op-amp via geometric programming
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
δ-complete decision procedures for satisfiability over the reals
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
dReal: an SMT solver for nonlinear theories over the reals
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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Certain formal verification tasks require reasoning about Boolean combinations of non-linear arithmetic constraints over the real numbers. In this paper, we present a new technique for satisfiability solving of Boolean combinations of non-linear constraints that are convex. Our approach applies fundamental results from the theory of convex programming to realize a satisfiability modulo theory (SMT) solver. Our solver, CalCS, uses a lazy combination of SAT and a theory solver. A key step in our algorithm is the use of complementary slackness and duality theory to generate succinct infeasibility proofs that support conflict-driven learning. Moreover, whenever non-convex constraints are produced from Boolean reasoning, we provide a procedure that generates conservative approximations of the original set of constraints by using geometric properties of convex sets and supporting hyperplanes. We validate CalCS on several benchmarks including formulas generated from bounded model checking of hybrid automata and static analysis of floating-point software.