Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
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Communications of the ACM
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Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
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Journal of Artificial Intelligence Research
A Gröbner basis approach to CNF-formulae preprocessing
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Boolean Gröbner bases in SAT solving
ACM Communications in Computer Algebra
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We extend clause learning as performed by most modern SAT Solvers by integrating the computation of Boolean Gröbner bases into the conflict learning process. Instead of learning only one clause per conflict, we compute and learn additional binary clauses from a Gröbner basis of the current conflict. We used the Gröbner basis engine of the logic package Redlog contained in the computer algebra system Reduce to extend the SAT solver MiniSAT with Gröbner basis learning. Our approach shows a significant reduction of conflicts and a reduction of restarts and computation time on many hard problems from the SAT 2009 competition.