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arXiv · 2306.10337

Notes on "Bounds on BDD-Based Bucket Elimination''

Randal E. Bryant
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Abstract

This paper concerns Boolean satisfiability (SAT) solvers based on Ordered Binary Decision Diagrams (BDDs), especially those that can generate proofs of unsatisfiability. Mengel (arXiv:2306.00886) has presented a theoretical analysis that a BDD-based SAT solver can generate a proof of unsatisfiability for the pigeonhole problem (PHP$_n$) in polynomial time, even when the problem is encoded in the standard ``direct'' form. His approach is based on bucket elimination, using different orderings for the variables in the BDDs than in the buckets. We show experimentally that these proofs scale as $O(n^5)$. We also confirm the exponential scaling that occurs when the same variable ordering is used for the BDDs as for the buckets.

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Randal E. Bryant. 2023-06-17. Notes on "Bounds on BDD-Based Bucket Elimination''. https://arxiv.org/abs/2306.10337

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