Compiling Finite Linear CSP into SAT

  • Naoyuki Tamura
  • Akiko Taga
  • Satoshi Kitagawa
  • Mutsunori Banbara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4204)


In this paper, we propose a method to encode Constraint Satisfaction Problems (CSP) and Constraint Optimization Problems (COP) with integer linear constraints into Boolean Satisfiability Testing Problems (SAT) . The encoding method is basically the same with the one used to encode Job-Shop Scheduling Problems by Crawford and Baker. Comparison xa is encoded by a different Boolean variable for each integer variable x and integer value a. To evaluate the effectiveness of this approach, we applied the method to Open-Shop Scheduling Problems (OSS) . All 192 instances in three OSS benchmark sets are examined, and our program found and proved the optimal results for all instances including three previously undecided problems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Naoyuki Tamura
    • 1
  • Akiko Taga
    • 2
  • Satoshi Kitagawa
    • 2
  • Mutsunori Banbara
    • 1
  1. 1.Information Science and Technology CenterKobe UniversityJapan
  2. 2.Graduate School of Science and TechnologyKobe UniversityJapan

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