Optimized CNF Encoding for Sudoku Puzzles

A Sudoku puzzle can be regarded as a propositional SAT problem. Various encodings are known for encoding Sudoku as a Conjunctive Normal Form(CNF) formula. Using these encodings for large Sudoku puzzles, however, generates too many clauses, which impede the performance of state-of-the-art SAT solvers. This paper presents an optimized CNF encoding in order to deal with large instances of Sudoku puzzles. We use fixed cells in Sudoku to remove obvious redundancies during the encoding phase. This results in reducing the number of clauses in the CNF encoding and a significant speedup in the SAT solving time.