Combining Symbolic Constraint Solvers on Algebraic Domains

@article{Kirchner1994CombiningSC,
  title={Combining Symbolic Constraint Solvers on Algebraic Domains},
  author={H{\'e}l{\`e}ne Kirchner and Christophe Ringeissen},
  journal={J. Symb. Comput.},
  year={1994},
  volume={18},
  pages={113-155}
}
Abstract In the context of constraint logic programming and theorem proving, the development of constraint solvers on algebraic domains and their combination is of prime interest. As an example, a constraint solver in finite algebras is presented for a constraint language including for instance equations, disequations and inequations. By extending techniques used for the combination of unification in disjoint equational theories, we show how to combine constraint solvers on different algebraic… 
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56 Citations
Background Citations
9
Methods Citations
5

56 Citations

Citation Type

Citation Type

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TLDR
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An Open Automated Framework for Constraint Solver Extension: the SoleX Approach
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The paper introduces the notion of a “free amalgamated product” as a possible solution to the first problem of how to treat “mixed” constraints, and defines so-called simply-combinable structures (SC-structures), which contain many solution structures used in constraint logic programming.
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TLDR
SoleX is a mechanism for extending constraint solvers in order to handle new function symbols on the computation domain by building two kinds of rule-based transformations: domain independent rules for symbolically processing constraints with additional function symbols and rules for completing the information on the domain with the usual interpretation of these additional functions.
Combination of Constraint Solving Techniques: An Algebraic POint of View
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This paper isolates an abstract algebraic property of free algebras—called combinability—that clarifies why the combination method applies to such algebraes, and introduces a new proof method that depends on abstract notions and results from universal algebra, as opposed to technical manipulations of terms.
Combination of Constraint Solvers for Free and Quasi-Free Structures
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A view of constraint programming based on the notion of rewriting controlled by strategies allows us to describe in a unified way the constraint solving mechanism as well as the meta-language needed to manipulate the constraints.
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An Environment for Designing/Executing Constraint Solver Collaborations
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  • Computer Science
    Electron. Notes Theor. Comput. Sci.
  • 1998
On the cooperation of the constraint domains ℋ, ℛ, and ℱ in CFLP
TLDR
The computational model has been proved sound and complete w.r.t. the declarative semantics provided by the CFLP scheme, while the implemented system has been tested with a set of benchmarks and shown to behave quite efficiently in comparison to the closest related approach.
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