WO2000055753A8 - Satisfiability algorithms and finite quantification - Google Patents

Satisfiability algorithms and finite quantification

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Publication number
WO2000055753A8
WO2000055753A8 PCT/US2000/006218 US0006218W WO0055753A8 WO 2000055753 A8 WO2000055753 A8 WO 2000055753A8 US 0006218 W US0006218 W US 0006218W WO 0055753 A8 WO0055753 A8 WO 0055753A8
Authority
WO
WIPO (PCT)
Prior art keywords
sub
search
algorithms
quantified
research
Prior art date
Application number
PCT/US2000/006218
Other languages
French (fr)
Other versions
WO2000055753A2 (en
Inventor
Matthew L Ginsberg
Andrew J Parkes
Original Assignee
Oregon State
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Oregon State filed Critical Oregon State
Publication of WO2000055753A2 publication Critical patent/WO2000055753A2/en
Publication of WO2000055753A8 publication Critical patent/WO2000055753A8/en

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

Abstract

La présente invention concerne l'amélioration des algorithmes de satisfaisabilité existants par modification de la représentation du problème qui exploite la structure des problèmes naturels. On considère plus particulièrement les algorithmes communs de satisfaisabilité, et notamment les WSAT et RELSAT. Chacun de ces algorithmes implique l'exécution, au moins une fois, d'un calcul spécifique, ou "sous-recherche", dans lequel l'algorithme recherche, dans la théorie originale, des clauses fondamentales satisfaisant l'une quelconque des propriétés numériques. Dans le cas des problèmes réalistes, l'invention fait que le temps passé en sous-recherche constitue une quantité négligeable par rapport à l'investissement représenté par le calcul de l'algorithme. De fait, l'invention représente la sous-recherche en termes de S(C,P,us), auquel cas les réalisations fondamentales de C présentent des littéraux u non valorisés par P pour des littéraux s vérifiés pour les valeurs attribuées à P. Cette représentation permet l'exécution d'une recherche intelligente pour résoudre les problèmes de sous-recherche posés en termes de S(C,P,u,s). La sous-recherche intelligente procède par attribution de valeurs de vérité, à des atomes, de façon à éliminer des ensembles de liaisons avec des variables universellement quantifiées dans les limites d'une contrainte clausale quantifiée. Ces liaisons s'éliminent d'ailleurs d'elles-mêmes du fait qu'elles ne peuvent pas satisfaire à une proposition spécifique. De plus, il reste possible de faire une remontée à partir des choix pauvres à l'occasion d'une recherche de liaisons aboutissant à des variables dans les limites des clauses quantifiées. D'une façon générale, la sous-recherche intelligente permet de réduire le temps de vérification des problèmes de O(D<U>) à O(D< alpha U>) pour tout alpha <1.The present invention relates to the improvement of existing satisfiability algorithms by modifying the representation of the problem which exploits the structure of natural problems. We consider more particularly the common satisfiability algorithms, in particular the WSAT and RELSAT. Each of these algorithms involves the execution, at least once, of a specific calculation, or "sub-search", in which the algorithm searches, in the original theory, for fundamental clauses satisfying any of the numerical properties . In the case of realistic problems, the invention makes the time spent in sub-research constituting a negligible quantity compared to the investment represented by the calculation of the algorithm. In fact, the invention represents the sub-search in terms of S (C, P, us), in which case the fundamental realizations of C present literals u not valued by P for literals s verified for the values assigned to P. This representation allows the execution of an intelligent search to solve the sub-search problems posed in terms of S (C, P, u, s). Intelligent sub-research proceeds by assigning truth values to atoms so as to eliminate sets of bonds with universally quantified variables within the limits of a quantified clausal constraint. These links are also eliminated by themselves because they cannot satisfy a specific proposition. In addition, it is still possible to go back from poor choices when looking for links leading to variables within the limits of quantified clauses. Generally speaking, intelligent sub-research makes it possible to reduce the time for checking problems from O (D <U>) to O (D <alpha U>) for any alpha <1.

PCT/US2000/006218 1999-03-09 2000-03-08 Satisfiability algorithms and finite quantification WO2000055753A2 (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US12353799P 1999-03-09 1999-03-09
US60/123,537 1999-03-09

Publications (2)

Publication Number Publication Date
WO2000055753A2 WO2000055753A2 (en) 2000-09-21
WO2000055753A8 true WO2000055753A8 (en) 2001-11-15

Family

ID=22409265

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US2000/006218 WO2000055753A2 (en) 1999-03-09 2000-03-08 Satisfiability algorithms and finite quantification

Country Status (2)

Country Link
US (1) US6556978B1 (en)
WO (1) WO2000055753A2 (en)

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US7062478B1 (en) * 2002-03-20 2006-06-13 Resolutionebs, Inc. Method and apparatus using automated rule processing to configure a product or service
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US20040034613A1 (en) * 2002-07-23 2004-02-19 Xerox Corporation System and method for dynamically generating a style sheet
US7010746B2 (en) * 2002-07-23 2006-03-07 Xerox Corporation System and method for constraint-based document generation
US7487445B2 (en) * 2002-07-23 2009-02-03 Xerox Corporation Constraint-optimization system and method for document component layout generation
US7171393B2 (en) * 2003-07-22 2007-01-30 International Business Machines Corporation Solving constraint satisfaction problems using variable-range hopping
US7565337B2 (en) * 2003-09-29 2009-07-21 Huelsman David L Batch validation method, apparatus, and computer-readable medium for rule processing
US7587380B2 (en) * 2003-09-29 2009-09-08 Huelsman David L Rule processing method, apparatus, and computer-readable medium to generate valid combinations for selection
US7552102B2 (en) * 2003-09-29 2009-06-23 Huelsman David L Rule processing method, apparatus, and computer-readable medium to provide improved selection advice
US20050187905A1 (en) * 2004-02-05 2005-08-25 Dixon Heidi E. Database manipulations using group theory
US7440942B2 (en) * 2004-02-05 2008-10-21 The State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of The University Of Oregon Database manipulations using group theory
US7194710B2 (en) * 2004-03-23 2007-03-20 Fujitsu Limited Scheduling events in a boolean satisfiability (SAT) solver
GB0407260D0 (en) * 2004-03-31 2004-05-05 Ibm Accelerated solution of constraint satisfaction problems by partioning of the variable space
US7734559B2 (en) * 2004-09-28 2010-06-08 Huelsman David L Rule processing method and apparatus providing exclude cover removal to simplify selection and/or conflict advice
US7333968B2 (en) * 2005-08-17 2008-02-19 International Business Machines Corporation Conditional CSP solving using constraint propagation
US20070174781A1 (en) * 2006-01-25 2007-07-26 Catalog Data Solutions Parameter visualization
US7562055B2 (en) * 2006-09-18 2009-07-14 International Business Machines Corporation Resolve trace minimization
US8069127B2 (en) * 2007-04-26 2011-11-29 21 Ct, Inc. Method and system for solving an optimization problem with dynamic constraints
US8140459B2 (en) 2008-02-21 2012-03-20 Microsoft Corporation Relevancy propagation for efficient theory combination
US9489221B2 (en) 2008-06-25 2016-11-08 Microsoft Technology Licensing, Llc Matching based pattern inference for SMT solvers
US8020125B1 (en) * 2008-09-10 2011-09-13 Cadence Design Systems, Inc. System, methods and apparatus for generation of simulation stimulus
JP2023037180A (en) * 2021-09-03 2023-03-15 株式会社豊田自動織機 Control device and control method of physical distribution warehouse

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US6031984A (en) 1998-03-09 2000-02-29 I2 Technologies, Inc. Method and apparatus for optimizing constraint models

Also Published As

Publication number Publication date
WO2000055753A2 (en) 2000-09-21
US6556978B1 (en) 2003-04-29

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