Some results and experiments in programming techniques for propositional logic
Computers and Operations Research - Special issue: Applications of integer programming
On the complexity of cutting-plane proofs
Discrete Applied Mathematics
Integer and combinatorial optimization
Integer and combinatorial optimization
Many hard examples for resolution
Journal of the ACM (JACM)
Algorithms for testing the satisfiability of propositional formulae
Journal of Logic Programming
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Logic programming with pseudo-Boolean constraints
Constraint logic programming
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Computers and Operations Research
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
Improvements to propositional satisfiability search algorithms
Improvements to propositional satisfiability search algorithms
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Hard problems for CSP Algorithms
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Cuting Plane Versus Frege Proof Systems
CSL '90 Proceedings of the 4th Workshop on Computer Science Logic
Combining linear programming and satisfiability solving for resource planning
The Knowledge Engineering Review
A scheme for unifying optimization and constraint satisfaction methods
The Knowledge Engineering Review
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Solving linear pseudo-Boolean constraint problems with local search
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
A complexity analysis of space-bounded learning algorithms for the constraint satisfaction problem
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
A fast pseudo-boolean constraint solver
Proceedings of the 40th annual Design Automation Conference
Inference methods for a pseudo-boolean satisfiability solver
Eighteenth national conference on Artificial intelligence
On the intersection of AI and OR
The Knowledge Engineering Review
The Knowledge Engineering Review
Bridging the gap between planning and scheduling
The Knowledge Engineering Review
On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Generalizing Boolean satisfiability I: background and survey of existing work
Journal of Artificial Intelligence Research
Generalizing Boolean satisfiability II: theory
Journal of Artificial Intelligence Research
Generalizing Boolean satisfiability III: implementation
Journal of Artificial Intelligence Research
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The recent effort to integrate techniques from the fields of artificial intelligence and operations research has been motivated in part by the fact that scientists in each group are often unacquainted with recent (and not so recent) progress in the other field. Our goal in this paper is to introduce the artificial intelligence community to pseudo-Boolean representation and cutting plane proofs, and to introduce the operations research community to restricted learning methods such as relevance-bounded learning. Complete methods for solving satisfiability problems are necessarily bounded from below by the length of the shortest proof of unsatisfiability; the fact that cutting plane proofs of unsatisfiability can be exponentially shorter than the shortest resolution proof can thus in theory lead to substantial improvements in the performance of complete satisfiability engines. Relevance-bounded learning is a method for bounding the size of a learned constraint set. It is currently the best artificial intelligence strategy for deciding which learned constraints to retain and which to discard. We believe these two elements or some analogous form of them are necessary ingredients to improving the performance of satisfiability algorithms generally. We also present a new cutting plane proof of the pigeonhole principle that is of size n2, and show how to implement some intelligent backtracking techniques using pseudo-Boolean representation.