An efficient finite-domain constraint solver for circuits
Proceedings of the 41st annual Design Automation Conference
When do bounds and domain propagation lead to the same search space?
ACM Transactions on Programming Languages and Systems (TOPLAS)
Contraint-Based Combinators for Local Search
Constraints
Programming finite-domain constraint propagators in Action Rules
Theory and Practice of Logic Programming
Propagating dense systems of integer linear equations
Proceedings of the 2007 ACM symposium on Applied computing
Exploiting Common Subexpressions in Numerical CSPs
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Efficient constraint propagation engines
ACM Transactions on Programming Languages and Systems (TOPLAS)
An abstract domain extending difference-bound matrices with disequality constraints
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Action rules for programming constraint propagators and interactive user interfaces
INAP'01 Proceedings of the Applications of prolog 14th international conference on Web knowledge management and decision support
Solving the salinity control problem in a potable water system
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Lazy clause generation reengineered
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
The complexity of integer bound propagation
Journal of Artificial Intelligence Research
Maximising the net present value for resource-constrained project scheduling
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The gauge domain: scalable analysis of linear inequality invariants
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
View-based propagator derivation
Constraints
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Propagation based finite domain solvers provide a general mechanism for solving combinatorial problems. Different propagation methods can be used in conjunction by communicating through the domains of shared variables. The flexibility that this entails has been an important factor in the success of propagation based solving for solving hard combinatorial problems. In this paper we investigate how linear integer constraints should be represented in order that propagation can determine strong domain information. We identify two kinds of substitution which can improve propagation solvers, and can never weaken the domain information. This leads us to an alternate approach to propagation based solving where the form of constraints is modified by substitution as computation progresses. We compare and contrast a solver using substitution against an indexical based solver, the current method of choice for implementing propagation based constraint solvers, identifying the relative advantages and disadvantages of the two approaches. In doing so, we investigate a number of choices in propagation solvers and their effects on a suite of benchmarks.