Computing Science Group THE ORDER ENCODING: FROM TRACTABLE CSP TO TRACTABLE SAT

Many mathematical and practical problems can be expressed as constraint satisfaction problems (CSPs). One way to solve a CSP instance is to encode it into SAT and use a SAT-solver. However, important information about the problem can get lost during the translation stage. For example, although the general constraint satisfaction problem is known to be NP-complete, there are some classes of CSP instances that have been shown to be tractable. These include the classes of CSP instances that contain only max-closed or connected-row-convex constraints. In this paper we show that translating such instances using some common standard encodings results in SAT instances which do not fall into known tractable classes. However, translating such instances using the order encoding results in SAT instances that do fall into known tractable classes. Moreover, modern clause learning SAT-solvers can then solve them efficiently. Hence, we give a theory-based argument to prefer the order encoding for certain families of constraint satisfaction problems. ∗An extended abstract is published in Theory and Applications of Satisfiability Testing SAT2011. Further copies of this Research Report may be obtained from the Librarian, Oxford University, Department of Computer Science, Computing Science Group, Wolfson Building, Parks Road, Oxford OX1 3QD, England (Telephone: +44-1865-273837, Email: [email protected]).