NDLI: Resolution cannot polynomially simulate compressed-BFS

Content Provider	Springer Nature Link
Author	Motter, DoRon B. Roy, Jarrod A. Markov, Igor L.
Copyright Year	2005
Abstract	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 Θ(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.
Starting Page	121
Ending Page	156
Page Count	36
File Format	PDF
ISSN	10122443
Journal	Annals of Mathematics and Artificial Intelligence
Volume Number	44
Issue Number	1-2
e-ISSN	15737470
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computer Science Artificial Intelligence (incl. Robotics) Mathematics Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence

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