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Redundant Sudoku rules

Published online by Cambridge University Press:  30 October 2012

BART DEMOEN  and
MARIA GARCIA DE LA BANDA
BART DEMOEN
Affiliation:
Department of Computer Science, KU Leuven, Belgium (e-mail: bart.demoen@cs.kuleuven.be)
MARIA GARCIA DE LA BANDA
Affiliation:
Faculty of Information Technology, Monash University, Australia (e-mail: Maria.GarciaDeLaBanda@monash.edu)
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Abstract

The rules of Sudoku are often specified using 27 all_different constraints, referred to as the big constraints. Using graphical proofs and exploratory logic programming, the following main and new result is obtained: Many subsets of six of these big constraints are redundant (i.e., they are entailed by the remaining 21 constraints), and six is maximal (i.e., removing more than six constraints is not possible while maintaining equivalence). The corresponding result for binary inequality constraints, referred to as the small constraints, is stated as a conjecture.

Keywords

Sudokuall_different constraintsinequalitiesmaximal redundancy
Type
Technical Notes
Information
Theory and Practice of Logic Programming , Volume 14 , Issue 3 , May 2014 , pp. 363 - 377
Copyright
Copyright © Cambridge University Press 2012 

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References

Demoen, B. and Garcia de la Banda, M. 2012. Maximal Sets of Redundant Constraints in Latin Square. Monash University, no. 2012/269. Technical Report.Google Scholar
Ist, I. L., Lynce, I. and Ouaknine, J. 2006. Sudoku as a SAT problem. Proceedings of the 9th International Symposium on Artificial Intelligence and Mathematics (AIMATH 2006), Fort Lauderdale, FL, USA. Springer, New York, USA.Google Scholar
Jussien, N. 2007. A to Z of SUDOKU. ISTE, London.Google Scholar
Kwon, G. and Jain, H. 2006. Optimized CNF encoding for Sudoku puzzles. In Short paper presentation at the 13th International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR 2006).Google Scholar
McGuire, G., Tugemann, B. and Civario, G. 2012. There is no 16-clue Sudoku: Solving the Sudoku minimum number of clues problem. CoRR abs/1201.0749.Google Scholar
Metodi, A. and Codish, M. 2012. Compiling finite domain constraints to SAT with BEE . Theory and Practice of Logic Programming 12, 4–5, 445–464.Google Scholar
Royle, G. Minimum Sudoku. Accessed September 2012. URL: http://school.maths.uwa.edu.au/∼gordon/sudokumin.php.Google Scholar
Wikipedia. n.d. Sudoku. Accessed September 2012. URL: http://en.wikipedia.org/wiki/Sudoku.Google Scholar