Sufficient and necessary conditions for solution finding in valuation-based systems
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to li...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/168518 |
| Acceso en línea: | https://hdl.handle.net/2117/168518 https://dx.doi.org/10.1016/j.ijar.2019.08.006 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebra Àlgebra Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Sumario: | Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to linear equation systems. Many widely used dynamic programming algorithms for optimization problems rely on low treewidth decompositions and can be understood as particular cases of a single algorithmic scheme for finding solutions in a valuation algebra. The most encompassing description of this algorithmic scheme to date has been proposed by Pouly and Kohlas together with sufficient conditions for its correctness. Unfortunately, the formalization relies on a theorem for which we provide counterexamples. In spite of that, the mainline of Pouly and Kohlas’ theory is correct, although some of the necessary conditions have to be revised. In this paper we analyze the impact that the counter-examples have on the theory, and rebuild the theory providing correct sufficient conditions for the algorithms. Furthermore, we also provide necessary conditions for the algorithms, allowing for a sharper characterization of when the algorithmic scheme can be applied. |
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