Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
Two-level logic minimization: an overview
Integration, the VLSI Journal
Basic graph theory: paths and circuits
Handbook of combinatorics (vol. 1)
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
An experimental study of an opportunistic index
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A machine program for theorem-proving
Communications of the ACM
Investigations on autark assignments
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
A proof engine approach to solving combinational design automation problems
Proceedings of the 39th annual Design Automation Conference
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Faster SAT and smaller BDDs via common function structure
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
A Compressed Breadth-First Search for Satisfiability
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Inference methods for a pseudo-boolean satisfiability solver
Eighteenth national conference on Artificial intelligence
Solving Graph Optimization Problems with ZBDDs
EDTC '97 Proceedings of the 1997 European conference on Design and Test
Multi-resolution on compressed sets of clauses
ICTAI '00 Proceedings of the 12th IEEE International Conference on Tools with Artificial Intelligence
Understanding the power of clause learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Solving difficult instances of Boolean satisfiability in the presence of symmetry
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
SymChaff: a structure-aware satisfiability solver
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
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Many algorithms for Boolean satisfiability (SAT) work within the framework of resolution as a proof system, and thus on unsatisfiable instances they can be viewed as attempting to find proofs by resolution. However it has been known since the 1980s that every resolution proof of the pigeonhole principle (PHPnm), suitably encoded as a CNF instance, includes exponentially many steps [18]. Therefore SAT solvers based upon the DLL procedure [12] or the DP procedure [13] must take exponential time. Polynomial-sized proofs of the pigeonhole principle exist for different proof systems, but general-purpose SAT solvers often remain confined to resolution. This result is in correlation with empirical evidence. Previously, we introduced the Compressed-BFS algorithm to solve the SAT decision problem. In an earlier work [27], an implementation of a Compressed-BFS algorithm empirically solved $\overline{\mathrm{PHP}_{n}^{n+1}}$ instances in 驴(n4) time. Here, we add to this claim, and show analytically that these instances are solvable in polynomial time by Compressed-BFS. Thus the class of tautologies efficiently provable by Compressed-BFS is different than that of any resolution-based procedure. We hope that the details of our complexity analysis shed some light on the proof system implied by Compressed-BFS. Our proof focuses on structural invariants within the compressed data structure that stores collections of sets of open clauses during the Compressed-BFS algorithm. We bound the size of this data structure, as well as the overall memory, by a polynomial. We then use this to show that the overall runtime is bounded by a polynomial.