International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

Overlapping Alldiff constraints: SAT versus CSP encoding application to the Sudoku

Eric Monfroy1,2*, Broderick Crawford1,3, Ricardo Soto3,4 and Fernando Paredes5      
1Universidad Técnica Federico Santa María, Department, de Informática, Av. España 1680, Valparaíso, Chile. 2CNRS, LINA, Université de Nantes, France. 3Pontificia Universidad Católica de Valparaíso, Chile. 4Universidad Autónoma de Chile, Chile. 5Escuela de Ingeniería Industrial, Universidad Diego Portales, Santiago, Chile.  
Email: [email protected]

  •  Accepted: 18 August 2011
  •  Published: 23 October 2011


Constraint satisfaction problems (CSP) or Boolean satisfiability problem (SAT) are two well-known paradigms to model and solve combinatorial problems. Modeling and resolution of CSP is often strengthened by global constraints (e.g., Alldiff constraint). This paper highlights two different ways of handling specific structural information: a uniform propagation framework to handle (interleaved) Alldiff constraints with some CSP reduction rules and a SAT encoding of these rules that preserves the reduction properties of CSP. We illustrate our approach on the well-known Sudoku puzzle which presents 27 overlapping Alldiff constraints in its 9 × 9 standard size. We also present some preliminary results we obtained in CHR, GeCode and Zchaff.


Key words: Boolean satisfiability problem (SAT), computer science, decision support, constraint programming, global constraint, automated reasoning.