Disjunctive programming: properties of the convex hull of feasible points
Discrete Applied Mathematics
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Dichotomic Search Protocols for Constrained Optimization
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
The LPSAT engine & its application to resource planning
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Constraint integer programming: a new approach to integrate CP and MIP
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
On SAT modulo theories and optimization problems
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Satisfiability modulo the theory of costs: foundations and applications
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
A modular approach to MaxSAT modulo theories
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
HVC'12 Proceedings of the 8th international conference on Hardware and Software: verification and testing
Symbolic optimization with SMT solvers
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories of practical interest (e.g., linear arithmetic, arrays, bit-vectors). Surprisingly, very little work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any work on SMT solvers able to produce solutions which minimize cost functions over arithmetical variables. This is unfortunate, since some problems of interest require this functionality. In this paper we start filling this gap. We present and discuss two general procedures for leveraging SMT to handle the minimization of ${\mathcal LA}$ (ℚ) cost functions, combining SMT with standard minimization techniques. We have implemented the procedures within the MathSAT SMT solver. Due to the absence of competitors in AR and SMT domains, we have experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP), which is closest in spirit to our domain, on sets of problems which have been previously proposed as benchmarks for the latter tools. The results show that our tool is very competitive with, and often outperforms, these tools on these problems, clearly demonstrating the potential of the approach.