QuadraticDirect Encoding vs. LinearOrderEncoding A One-out-of-N Transformation on CNF

The translation from finite CSPs into SAT has been studied intensively. Common encodings for variable domains are the compact, direct and order encoding. The direct encoding needs a quadratic number of clauses for encoding a domain in SAT whereas the order encoding uses only linearly many. We introduce a conversion for domains from the direct encoding to the order encoding on the CNF level by extracting the encoded domains and replacing the related clauses by the order encoding and a mapping between them. The transformation keeps the model for the original formula and transforming domains with more than 8 elements results in less clauses in the formula. Experiments showed that our SAT solver riss can solve the transformed instances with domains greater than 7 from the SAT Competition 2009 Application with 3.4% less run time. On 105 crafted instances riss could solve 55 instead of 58 instances, but the average run time decreased by 30%. Results for PrecoSAT, clasp and march hi will be presented as well, showing that the transformation boosts the performance of CDCL solvers.