Mixed logical-linear programming
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Logic, Optimization, and Constraint Programming
INFORMS Journal on Computing
Volume Computation for Boolean Combination of Linear Arithmetic Constraints
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Search space reduction and Russian Doll search
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
CAV'07 Proceedings of the 19th international conference on Computer aided verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
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
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TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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In a classical constrained optimization problem, the logical relationship among the constraints is normally the logical conjunction. However, in many real applications, the relationship among the constraints might be more complex. This paper investigates a generalized class of optimization problems whose constraints are connected by various kinds of logical operators in addition to conjunction. Such optimization problems have been rarely studied in literature in contrast to the classical ones. A framework which integrates classical optimization procedures into the DPLL(T) architecture for solving Satisfiability Modulo Theories (SMT) problems is proposed. Two novel techniques for improving the solving efficiency w.r.t. linear arithmetic theory are also presented. Experiments show that the proposed techniques are quite effective.