Parallel Variable Elimination on CNF Formulas

2013 ◽  
pp. 61-73 ◽  
Author(s):  
Kilian Gebhardt ◽  
Norbert Manthey
Keyword(s):  
Variable Elimination ◽  
Cnf Formulas

On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances

2017 ◽  
Vol 18 (3) ◽  
pp. 1-46
Author(s):  
Ronald De Haan ◽  
Iyad Kanj ◽  
Stefan Szeider
Keyword(s):  
Parameterized Complexity ◽  
Cnf Formulas

Practical Tools for Reasoning About Linear Constraints

1991 ◽  
Vol 15 (3-4) ◽  
pp. 357-379
Author(s):  
Tien Huynh ◽  
Leo Joskowicz ◽  
Catherine Lassez ◽  
Jean-Louis Lassez
Keyword(s):  
Logic Programming ◽  
Intelligent Systems ◽  
Optimization Problem ◽  
Spatial Reasoning ◽  
Quantifier Elimination ◽  
Canonical Representation ◽  
Linear Constraints ◽  
Practical Applications ◽  
Variable Elimination ◽  
Fourier Algorithm

We address the problem of building intelligent systems to reason about linear arithmetic constraints. We develop, along the lines of Logic Programming, a unifying framework based on the concept of Parametric Queries and a quasi-dual generalization of the classical Linear Programming optimization problem. Variable (quantifier) elimination is the key underlying operation which provides an oracle to answer all queries and plays a role similar to Resolution in Logic Programming. We discuss three methods for variable elimination, compare their feasibility, and establish their applicability. We then address practical issues of solvability and canonical representation, as well as dynamical updates and feedback. In particular, we show how the quasi-dual formulation can be used to achieve the discriminating characteristics of the classical Fourier algorithm regarding solvability, detection of implicit equalities and, in case of unsolvability, the detection of minimal unsolvable subsets. We illustrate the relevance of our approach with examples from the domain of spatial reasoning and demonstrate its viability with empirical results from two practical applications: computation of canonical forms and convex hull construction.

scholarly journals Variable elimination for influence diagrams with super value nodes

2010 ◽  
Vol 51 (6) ◽  
pp. 615-631 ◽  
Author(s):  
Manuel Luque ◽  
Francisco Javier Díez
Keyword(s):  
Influence Diagrams ◽  
Variable Elimination

scholarly journals Generalizations of matched CNF formulas

2004 ◽  
Vol 43 (1-4) ◽  
pp. 223-238 ◽  
Author(s):  
Stefan Szeider
Keyword(s):  
Cnf Formulas

An Inverse Force Analysis of a Planar Two-Spring System

1994 ◽  
Author(s):  
Thomas M. Pigoski ◽  
Joseph Duffy
Keyword(s):  
The Other ◽  
Spring Stiffness ◽  
Force Analysis ◽  
Degree Polynomial ◽  
Real Solutions ◽  
Variable Elimination ◽  
Spring System ◽  
The Common ◽  
Resultant Length ◽  
Inverse Force

Abstract A closed-form inverse force analysis was performed on a planar two-spring system. The two springs were grounded to pivots at one end and attached to a common pivot at the other. A known force was applied to the common pivot of the system, and it was required to determine all of the assembly configurations. By variable elimination, a sixth degree polynomial in the resultant length of one spring was derived, and from this, six real solutions of the point of application of force were obtained. Following this, the applied force was incremented along a line and the six paths of the moving pivot were tracked starting from the zero-load configurations. An analysis of these results showed stability phenomena indicating the workspace of this system contained regions of negative spring stiffness and points of catastrophe.

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