伪布尔约束的最优基编码
Optimal Base Encodings for Pseudo-Boolean Constraints
摘要：
本文对最优基问题进行了形式化描述，提出了一种求解最优基问题的算法，并描述了该算法在SAT伪布尔约束编码中的应用。我们证明了我们的算法集成在伪布尔约束求解器MINISAT+的影响。实验表明，我们的算法规模的基础上，涉及的数字高达100万，改善了MINISAT+的限制，素数高达17。我们表明，虽然对于许多例子素数高达17做足够的，编码方面的最佳基地减少了CNF的大小，并提高了随后的SAT求解时间为许多例子。
英文摘要：
This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the Pseudo-Boolean constraint solver MINISAT+. Experimentation indicates that our algorithm scales to bases involving numbers up to 1,000,000, improving on the restriction in MINISAT+ to prime numbers up to 17. We show that, while for many examples primes up to 17 do suffice, encoding with respect to optimal bases reduces the CNF sizes and improves the subsequent SAT solving time for many examples.
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