Effective Lower Bounding Techniques for Pseudo-Boolean Optimization
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Solution and Optimization of Systems of Pseudo-Boolean Constraints
IEEE Transactions on Computers
Algorithms for Weighted Boolean Optimization
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
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
Automated reasoning in ALCQ via SMT
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Pseudo-Boolean Solving by incremental translation to SAT
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Active learning of combinatorial features for interactive optimization
LION'05 Proceedings of the 5th international conference on Learning and Intelligent Optimization
Solving generalized optimization problems subject to SMT constraints
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Optimization in SMT with LA(Q) cost functions
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Minimum satisfying assignments for SMT
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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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We extend the setting of Satisfiability Modulo Theories (SMT) by introducing a theory of costs ${\mathcal{C}}$, where it is possible to model and reason about resource consumption and multiple cost functions, e.g., battery, time, and space. We define a decision procedure that has all the features required for the integration withint the lazy SMT schema: incrementality, backtrackability, construction of conflict sets, and deduction. This naturally results in an SMT solver for the disjoint union of ${\mathcal{C}}$ and any other theory ${\mathcal{T}}$. This framework has two important applications. First, we tackle the problem of Optimization Modulo Theories: rather than checking the existence of a satisfying assignment, as in SMT, we require a satisfying assignment that minimizes a given cost function. We build on the decision problem for SMT with costs, i.e., finding a satisfying assigniment with cost within an admissibility range, and propose two algorithms for optimization. Second, we use multiple cost functions to deal with PseudoBoolean constraints. Within the ${\text{SMT}({\mathcal C})}$ framework, the effectively PseudoBoolean constraints are dealt with by the cost solver, while the other constraints are reduced to pure boolean reasoning. We implemented the proposed approach within the MathSAT SMT solver, and we experimentally evaluated it on a large set of benchmarks, also from industrial applications. The results clearly demonstrate the potential of the approach.