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Combination of constraint solving techniques: An algebraic point of view [chapter]

Franz Baader, Klaus U. Schulz
1995 Lecture Notes in Computer Science  
Complementing this logical point of view, the present paper isolates an abstract algebraic property of free algebras| called combinability|that clari es why our combination method applies to such algebras  ...  We use this algebraic point of view to introduce a new proof method that depends on abstract notions and results from universal algebra, as opposed to technical manipulations of terms (such as ordered  ...  In the present paper, we are only interested in solvability of constraints, and will thus usually take this logical point of view.  ... 
doi:10.1007/3-540-59200-8_69 fatcat:37vnnxzvyzbezajup2zv2qpbsu

Primal-dual interior-point Methods for Semidefinite Programming from an algebraic point of view, or: Using Noncommutativity for Optimization [article]

Konrad Schrempf
2020 arXiv   pre-print
richness of "non-commutative" search directions: (primal) feasible-interior-point methods.  ...  We shade a light on a rather surprising restriction in the non-commutative world (of semidefinite programming), namely "commutative" paths and propose a new family of solvers that is able to use the full  ...  Todd for hints on the literature and Birgit Janko for very valuable feedback on several drafts of this work.  ... 
arXiv:1812.10278v2 fatcat:7o6rnxyp2nbaleidgk5emtmsxq

Solving Boolean Combinations of Nonlinear Numerical Constraints

Xiao-Hui JI
2005 Journal of Software (Chinese)  
Many existing methods for solving such constraints are incomplete. A new method is presented in this paper to solve Boolean combinations of nonlinear numerical constraints completely.  ...  Constraints involving Boolean and numerical variables are used widely, but it is difficult to solve especially when they contain nonlinear numerical expressions.  ...  A Boolean combination of nonlinear numerical constraints can be viewed as an extension to a formula, in which a Boolean variable may be associated with a numerical constraint.  ... 
doi:10.1360/jos160659 fatcat:woi5fm6ojze4hj7zlj7al35cfe

Assertion checking by combined word-level ATPG and modular arithmetic constraint-solving techniques

Chung-Yang Huang, Kwang-Ting Cheng
2000 Proceedings of the 37th conference on Design automation - DAC '00  
Our approach combines structural, word-level automatic test pattern generation (ATPG) and modular arithmetic constraint-solving techniques to solve the constraints imposed by the target assertion property  ...  A prototype system has been built which consists of an industrial front-end HDL parser, a propertyto-constraint converter and the ATPG/arithmetic constraint-solving engine.  ...  This hybrid approach utilizes the strengths of both techniques in solving different kinds of constraints in the circuit.  ... 
doi:10.1145/337292.337333 dblp:conf/dac/HuangC00 fatcat:akxf7bdfmnfvfiwhrw2rannlwi

Singular and special points on quadrature domains from an algebraic geometric point of view

Björn Gustafsson
1988 Journal d'Analyse Mathematique  
(//, AL 1 ) with ju as in (1.1) and of order n. It is shown in [1] that dfi is a subset of an algebraic curve.  ...  forzE[0,Q close to Ck-)Combining this with the information about u near the origin it follows that if Ck is not a cusp point of dQ, then u \ Nk must have an interior local maximum on [0, Ck)-Since, by  ...  Then 2~1 /6 ^p < oo, J r = I r for r <p and we can choose a point (r 0 , T 0 )Eint <2 with r 0 </> so close to p so that p -r 0 <e(r 0 , T 0 ).  ... 
doi:10.1007/bf02791120 fatcat:hbeis2lr4rcp5nzfxsz4diahry

Algebraic Techniques for Gaussian Models [article]

Mathias Drton
2006 arXiv   pre-print
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps.  ...  This paper demonstrates such applications of algebraic geometry in selected examples of Gaussian models, thereby complementing the existing literature on models for discrete variables.  ...  If this parameterization is rational, as detailed in the following definition, then the resulting model can be studied taking an algebraic point of view.  ... 
arXiv:math/0610679v1 fatcat:nwn43r6x7bbbfmlgzqkld4nkqa

Symbolic simulation---techniques and applications

Randal E. Bryant
1990 Conference proceedings on 27th ACM/IEEE design automation conference - DAC '90  
In one simulation run, a symbolic simulator can compute what would require many runs of a traditional simulator.  ...  Symbolic simulation involves evaluating circuit behavior using special symbolic values to encode a range of circuit operating conditions.  ...  This gives us an algebra that satisfies all of the laws of a Boolean algebra.  ... 
doi:10.1145/123186.128296 dblp:conf/dac/Bryant90 fatcat:covuozf64jb4pmzqdmdfrkjtcq

Rewriting Techniques in the Constraint Solver

Jonathan Millen
2009 Electronical Notes in Theoretical Computer Science  
The constraint solver uses a free message algebra and a bounded-process network model with a Dolev-Yao attacker. These choices yield simplicity and decidability.  ...  Several of the design characteristics of this tool, and the reasons for them, are discussed and placed in perspective with other approaches.  ...  At this point we must face the main limitation of the constraint solver, and that is its bounded-process limitation.  ... 
doi:10.1016/j.entcs.2009.02.073 fatcat:uvt3p4oc3zf7vac5hpcbgwtkje

Diagram techniques for multiple view geometry

Alberto Ruiz, Pedro E Lopez-de-Teruel
2009 2009 IEEE 12th International Conference on Computer Vision  
Multilinear algebra is a powerful theoretical tool for visual geometry, but widespread usage of traditional typographical notation often hides its conceptual elegance and simplicity.  ...  In this paper we adapt standard tensor diagrammatic techniques to the specific requirements of visual geometry, so that geometric relations are represented by circuits which can be manipulated using simple  ...  To solve this problem we additively combine N with a rank-1 auxiliary camera which maps C to its image in the second view (the epipole e ).  ... 
doi:10.1109/iccv.2009.5459414 dblp:conf/iccv/RuizL09 fatcat:375vqvwgmjam3nxfrtbn4pecgq

Convex optimization techniques in system identification

Lieven Vandenberghe
2012 IFAC Proceedings Volumes  
In recent years there has been growing interest in convex optimization techniques for system identification and time series modeling.  ...  This interest is motivated by the success of convex methods for sparse optimization and rank minimization in signal processing, statistics, and machine learning, and by the development of new classes of  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.3182/20120711-3-be-2027.00244 fatcat:k4dxky3ktre47hoagl7smuskca

Incorporation of Artificial Intelligence Tutoring Techniques in Mathematics

Marios Pappas, Athanasios Drigas
2016 International Journal of Engineering Pedagogy (iJEP)  
Intelligent Tutoring Systems incorporate Artificial Intelligence techniques, in order to imitate a human tutor.  ...  of the last decade.  ...  A genetic algorithm is usually used as an optimization technique acting simultaneously on a wide set of points.  ... 
doi:10.3991/ijep.v6i4.6063 fatcat:c45bjwgr65hhdirzgjho2cbsmy

Appendix: Optimization Techniques [chapter]

2005 Risk Modeling, Assessment, and Management  
Three major simulation techniques can be identified. They are based on the use of a digital computer, an analog computer, or a hybrid computer (combination of digital and analog).  ...  In fact, any point on that constraint line will yield to an optimal solution.  ...  Appendix Optimization Techniques where x is an N-dimensional vector of decision variables defined over the N-dimensional EN Euclidean space, S,.  ... 
doi:10.1002/0471723908.app1 fatcat:ubkmmpitirhive5lwhyd7xzdt4

Scene modeling based on constraint system decomposition techniques

Wilczkowiak, Trombettoni, Jermann, Sturm, Boyer
2003 Proceedings Ninth IEEE International Conference on Computer Vision  
The approach is based on a dictionary of so-called r-methods, based on theorems of geometry, which can solve a subset of geometric constraints in a very efficient way.  ...  Our system can describe a large variety of linear and non-linear constraints in a flexible way.  ...  An r-method (see [12] and Definition 1) is a predefined routine used to solve a set of geometric constraints.  ... 
doi:10.1109/iccv.2003.1238458 dblp:conf/iccv/WilczkowiakTJSB03 fatcat:ytezc6sgf5biravk2ublbsmzba

Nonlinear microwave simulation techniques

Almudena Suarez
2015 2015 Integrated Nonlinear Microwave and Millimetre-wave Circuits Workshop (INMMiC)  
The methods will be applied to timely circuit examples that are demanding from the nonlinear analysis point of view.  ...  This stability analysis can also be combined with the use of auxiliary generators to simulate the circuit self-oscillation and predict qualitative changes in the solution under the continuous variation  ...  ACKNOWLEDGEMENT Author is grateful to Franco Ramírez, Sergio Sancho and Mabel Pontón from University of Cantabria.  ... 
doi:10.1109/inmmic.2015.7330374 fatcat:mgndezscundsne5svkuedby4ae

Combining constructive and equational geometric constraint-solving techniques

R. Joan-Arinyo, A. Soto-Riera
1999 ACM Transactions on Graphics  
This work reports on a hybrid method that combines two geometric constraint solving techniques: constructive and equational.  ...  In general, geometric constraint solving including functional relationships requires a general approach and appropriate techniques to achieve the expected functional capabilities.  ...  The approach we propose in this article combines native constructive geometric constraint solving techniques with algebraic equation solving without mapping one problem domain to the other.  ... 
doi:10.1145/300776.300780 fatcat:2i3u3kaebfdu7hytp2bc3czfwi
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