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Redundant Modeling for the QuasiGroup Completion Problem [chapter]

Iván Dotú, Alvaro del Val, Manuel Cebrián
2003 Lecture Notes in Computer Science  
The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, and the focus of much recent interest in the area of constraint programming. [5] reports that QCPs  ...  Our solution combines a number of known ideas -the use of redundant modeling [3] with primal and dual models of the problem connected by channeling constraints [13]-with some novel aspects, as well as  ...  as alldiff [8] -in solving quasigroup completion problems [9] .  ... 
doi:10.1007/978-3-540-45193-8_20 fatcat:rmzdtha7ybaqhhi727r4d2zhiy

Channeling Constraints and Value Ordering in the QuasiGroup Completion Problem

Iván Dotú, Alvaro del Val, Manuel Cebrián
2003 International Joint Conference on Artificial Intelligence  
Introduction The Quasigroup Completion Problem (QCP) is a very chal lenging benchmark among combinatorial problems, and a fo cus of much recent interest in the area of constraint program ming.  ...  Conclusions and Future Work We have shown that a pure CSP approach can handle quasigroup completion problems significantly larger than was thought possible, using appropriate models and value ordering  ... 
dblp:conf/ijcai/DotuVC03 fatcat:2pj524btcbh4noqyfs57n4mfmm

Page 7669 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
in the theory of quasigroups.  ...  needed for assignment completion.  ... 

A Randomization Strategy for Combinatorial Search

Hantao Zhang
2002 International Symposium on Artificial Intelligence and Mathematics  
Using the new strategy, we are able to solve several previously open quasigroup problems, which could not be solved using any existing SAT systems.  ...  This new strategy is implemented in SATO, an efficient implementation of the Davis-Putnam-Loveland method for SAT problems.  ...  Solving Open Quasigroup Problems Our real interests for developing the new strategy are on solving open quasigroup problems [22] .  ... 
dblp:conf/isaim/Zhang02 fatcat:53cnftf5n5eftnv25vcnkvk7um

Automatic Generation of Some Results in Finite Algebra

Masayuki Fujita, John K. Slaney, Frank Bennett
1993 International Joint Conference on Artificial Intelligence  
This is a report of the application of the Model Generation Theorem Prover developed at ICOT to problems in the theory of finite quasigroups. Several of the problems were pre viously open.  ...  We then present and discuss our machine-aided investi gation of seven problems concerning the exis tence of types of quasigroup.  ...  For finite domain problems such as n-queen problems and the Peiletier and Rudnicki problems, how ever, a weight strategy such as ours does not endanger completeness.  ... 
dblp:conf/ijcai/FujitaSB93 fatcat:sksqmpyw6zb3pn3adqn56lfghy

Balance and Filtering in Structured Satisfiable Problems (Preliminary Report)

Henry Kautz, Yongshao Ruan, Dimitris Achlioptas, Carla Gomes Bart Selman, Mark Stickel
2001 Electronic Notes in Discrete Mathematics  
New methods to generate hard random problem instances have driven progress on algorithms for deduction and constraint satisfaction. Recently Achlioptas et al.  ...  We also discuss the critical role of the problem encoding in the performance of both systematic and local search solvers.  ...  Achlioptas et al. (2000) described a generation model for satisfiable quasigroup completion problems called "quasigroups with holes" (QWH).  ... 
doi:10.1016/s1571-0653(04)00310-5 fatcat:p3ovbo6yhjaavgbm7t47hpozcy

PSATO: a Distributed Propositional Prover and its Application to Quasigroup Problems

1996 Journal of symbolic computation  
Several dozens of open problems in the study of quasigroups have been solved using PSATO.  ...  PSATO is based on the sequential SAT prover SATO, which is an efficient implementation of the Davis-Putnam algorithm. The masterslave model is used for communication.  ...  Acknowledgements We thank Bill McCune for providing us with the P4 scheme code of the master-slave model.  ... 
doi:10.1006/jsco.1996.0030 fatcat:zlqltbg7eradtoazeprk362que

SEM: a System for Enumerating Models

Jian Zhang, Hantao Zhang
1995 International Joint Conference on Artificial Intelligence  
To the best of our knowledge, SEM outperforms any other finite model generation system on many test problems.  ...  In this paper, we describe SEM, a System for Enumerating fi nite Models of first-order many-sorted theories.  ...  (The related identities are: QG7. (yx)y = x(yx); QG8. x(xy) = yx; and QG9. {(xy)y)y = x.) For the first two problems,2 it took several days for SEM to complete the search.  ... 
dblp:conf/ijcai/ZhangZ95 fatcat:qqnmatya6bbkbh5kk34vbhrrp4

Artificial intelligence and operations research: challenges and opportunities in planning and scheduling

2000 Knowledge engineering review (Print)  
, searching existing data sources, gathering end maintaining the data needed, and completing and reviewing the collection of information.  ...  REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0)88 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions  ...  showed the quasigroup completion problem to be NP-complete. In previous work, we identified a clear phase transition phenomenon for the quasigroup completion problem (Gomes and Selman 1997a) .  ... 
doi:10.1017/s0269888900001090 fatcat:ujl5jthik5akxaanwvh2jemldy

Heuristics for dynamically adapting propagation in constraint satisfaction problems

Kostas Stergiou
2009 AI Communications  
The success of this approach is based on the observation that propagation events for individual constraints in structured problems mostly occur in clusters of nearby revisions.  ...  Hence, parts of the search space where certain constraints are highly active can be identified and exploited paving the way for the informed use of constraint propagation techniques.  ...  An important aspect of the modelling process is the choice of propagation method for the various constraints in the problem.  ... 
doi:10.3233/aic-2009-0450 fatcat:d4quqgs3qvdjzm5hftzgqgth5e

Extending Unit Propagation Look-Ahead of DPLL Procedure [chapter]

2004 Lecture Notes in Computer Science  
The DPLL (Davis-Putnam-Logemann-Loveland) procedure is one of the most effective methods for solving SAT problems. It is well known that its efficiency depends on the choice of the branching rule.  ...  Experimental results of DVF+NVO branching rule on a number of real-world benchmark instances and quasigroup problems prove our approaches to be useful in many circumstances.  ...  Acknowledgments We would like to thank Andrew Slater for helping us to run the experiments.  ... 
doi:10.1007/978-3-540-28633-2_20 fatcat:mwaxvhq6ajft5gqu547ud6jpdq

Automatic Generation of Classification Theorems for Finite Algebras [chapter]

Simon Colton, Andreas Meier, Volker Sorge, Roy McCasland
2004 Lecture Notes in Computer Science  
, and the Gap computer algebra system to reduce the complexity of the problems given to Spass.  ...  We demonstrate the power of this approach by classifying loops, groups, monoids and quasigroups of various sizes.  ...  Acknowledgements We would like to thank Wendy Myrvold and colleagues for providing data on isomorphism classes for loops and quasigroups, Bill McCune for expert advice about Mace, Thomas Hillenbrand for  ... 
doi:10.1007/978-3-540-25984-8_30 fatcat:wngtz3c5hjag7ooafhlycresie

Proof Confluent Tableau Calculi [chapter]

Reiner Hähnle, Bernhard Beckert
1999 Lecture Notes in Computer Science  
This gives a formal justification why constraint MGTP is a complete procedure for many applications such as quasigroup problems.  ...  Let us call this (as usual) the strong completeness problem.  ... 
doi:10.1007/3-540-48754-9_7 fatcat:ajjhyyjfvreqrduwjyvg7l4r7a

Efficient SAT-Encoding of Linear CSP Constraints

Pedro Barahona, Steffen Hölldobler, Van-Hau Nguyen
2014 International Symposium on Artificial Intelligence and Mathematics  
In this paper we analyze the strengths and drawbacks of these encoding in the context of linear CSP problems and propose a new Sp-Or encoding, based on redundant modeling common in Constraint Programming  ...  The paper concludes with some guidelines regarding the choice of suitable SAT encodings for CSP problems, taking into account several features of these problems.  ...  Acknowledgment We are grateful to Amit Metodi for his fruitful supports, and to Inês Lynce for useful suggestions. We thank Carla Gomes for her kindly providing the QWH instances.  ... 
dblp:conf/isaim/BarahonaHN14 fatcat:5s3qy7mtyrdlvfqzqoidr6pozm

Groups, triality, and hyperquasigroups

Jonathan D.H. Smith
2012 Journal of Pure and Applied Algebra  
The concept of orthant structure is introduced, as a tool for recovering classical information from a hyperquasigroup.  ...  In the current paper, various connections between hyperquasigroups and groups are examined, on the basis of established connections between quasigroups and groups.  ...  Acknowledgement The author is grateful to anonymous referees for various suggestions concerning earlier drafts of the paper.  ... 
doi:10.1016/j.jpaa.2011.08.014 fatcat:avu5iyyk7veubmf27bf6iqrhha
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