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Exponential Bounds for DPLL below the Satisfiability Threshold
 in Proc. 15th ACMSIAM Symp. Discrete Algorithms
, 2004
"... We prove that for every k 4 there exists a constant r k such that a random kCNF formula F with n variables and #r k n# clauses is satisfiable with high probability, but every backtracking extension of ORDEREDDLL takes exponential time on F with uniformly positive probability. Combined with ..."
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Cited by 11 (2 self)
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We prove that for every k 4 there exists a constant r k such that a random kCNF formula F with n variables and #r k n# clauses is satisfiable with high probability, but every backtracking extension of ORDEREDDLL takes exponential time on F with uniformly positive probability. Combined
Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas
, 2004
"... DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satis ability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatis able formulas are equivalent to tree ..."
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Cited by 26 (3 self)
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DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satis ability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatis able formulas are equivalent to tree
XOR Satisfiability Solver Module for DPLL Integration
, 2010
"... Satisfiability solvers that are based on the DavisPutnamLogemannLoveland (DPLL) algorithm operate on propositional logic formulas in conjunctive normal form (CNF). Despite major improvements in solver technology, using only CNF does not seem to scale well for problem instances involving XOR exp ..."
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Satisfiability solvers that are based on the DavisPutnamLogemannLoveland (DPLL) algorithm operate on propositional logic formulas in conjunctive normal form (CNF). Despite major improvements in solver technology, using only CNF does not seem to scale well for problem instances involving XOR ex
A random constraint satisfaction problem that seems hard for DPLL
 In the Proceedings of SAT 2004
, 2004
"... Abstract. This paper discusses an NPcomplete constraint satisfaction problem which appears to share many of the threshold characteristics of SAT but is similar to XORSAT and so is easier to analyze. For example, the exact satisfiability threshold for this problem is known, and the problem has high ..."
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Cited by 5 (1 self)
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high resolution complexity. In this paper, we prove the problem appears hard for DPLL. Specifically, if we pick a problem instance at random with constraint density higher than some given threshold but below the satisfiability threshold, a DPLL backtracking algorithm using the unit clause heuristic
A Sharp Threshold in Proof Complexity Yields Lower Bounds for Satisfiability Search
"... We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small > 0 and > 2:28, random formulas consisting of (1 )n 2clauses and n 3clauses, which are known to be unsatisfiable almost certainly, almost certainly require resoluti ..."
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Cited by 13 (3 self)
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CNF formulas at ratios below the generally accepted range of the satisfiability threshold (and thus expected to be satisfiable almost certainly) cause natural DavisPutnam algorithms to take exponential time to find satisfying assignments. 1
Parameterized complexity of DPLL search procedures
 IN PROC. 14TH INTERNATIONAL CONFERENCE ON THEORY AND APPLICATIONS OF SATISFIABILITY TESTING. LECTURE NOTES IN COMPUTER SCIENCE SERIES
, 2011
"... We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a ProverDelayer game which models the running time of DPL ..."
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Cited by 12 (6 self)
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We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a ProverDelayer game which models the running time
Exponential Lower Bounds for a DPLL Attack against a OneWay Function Based on Expander Graphs
, 2008
"... This paper was written as a culmination of my work in the SUPERB 2008 Program at UC Berkeley, but is a work in progress. Please contact me at rachelmiller@virginia.edu for the most recent copy. Oded Goldreich’s 2000 paper “Candidate OneWay Functions Based on Expander Graphs ” [4] describes a funct ..."
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assumption about Goldreich’s function. DPLL is for Davis, Putnam, Logemann and Loveland, and many modern SAT solvers fit in the DPLL framework. For unsatisfiable instances, DPLL algorithms are subject to exponential lower bounds of treelike resolution proofs. However, few lower bounds exist for satisfiable
Results 1  10
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153,161