Constraints

, Volume 14, Issue 2, pp 254–272 | Cite as

Compiling finite linear CSP into SAT

  • Naoyuki Tamura
  • Akiko Taga
  • Satoshi Kitagawa
  • Mutsunori Banbara
Open Access
Article

Abstract

In this paper, we propose a new 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 (named order encoding) is basically the same as the one used to encode Job-Shop Scheduling Problems by Crawford and Baker. Comparison x ≤ a 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 the 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.

Keywords

Constraint satisfaction problems SAT encoding Open-shop scheduling problems 

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Copyright information

© The Author(s) 2008

Authors and Affiliations

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

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