Generic Solution Construction in Valuation-Based Systems

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6657)


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 notions of solutions. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to linear equation systems. Contrary to inference, there is no general algorithm to compute solutions in arbitrary valuation algebras. This paper states formal requirements for the presence of solutions and proposes a generic algorithm for solution construction based on the results of a previously executed inference scheme. We study the application of generic solution construction to semiring constraint systems, sparse linear systems and algebraic path problems and show that the proposed method generalizes various existing approaches for specific formalisms in the literature.


solution construction in valuation algebras local computation semiring constraint systems sparse matrix techniques 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Interdisciplinary Centre for Security, Reliability and TrustUniversity of LuxembourgLuxembourg

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