Recognizing unbounded integer programs
Operations Research
Solution of large-scale symmetric travelling salesman problems
Mathematical Programming: Series A and B
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Safe bounds in linear and mixed-integer linear programming
Mathematical Programming: Series A and B
Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Generalizing DPLL to Richer Logics
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
SAT modulo the theory of linear arithmetic: exact, inexact and commercial solvers
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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
Natural domain SMT: a preliminary assessment
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
An exact rational mixed-integer programming solver
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Cutting to the Chase solving linear integer arithmetic
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Synthesizing cyber-physical architectural models with real-time constraints
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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
Optimization in SMT with LA(Q) cost functions
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been applied to industrial synthesis and design problems with real-time constraints arising in the development of the Boeing 787. Many other problems ranging from operations research to software verification routinely involve linear constraints and optimization. Thus, a general ILP Modulo Theories framework has the potential to be widely applicable. The logical next step in the development of IMT and the main goal of this paper is to provide theoretical underpinnings. This is accomplished by means of BC(T), the Branch and Cut Modulo T abstract transition system. We show that BC(T) provides a sound and complete optimization procedure for the ILP Modulo T problem, as long as T is a decidable, stably-infinite theory. We compare a prototype of BC(T) against leading SMT solvers.