A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A lower bound for DLL algorithms for k-SAT (preliminary version)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
SAT Local Search Algorithms: Worst-Case Study
Journal of Automated Reasoning
Optimal myopic algorithms for random 3-SAT
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Pseudorandom generators in propositional proof complexity
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Lower Bounds for Polynomial Calculus: Non-Binomial Case
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Exponential bounds for DPLL below the satisfiability threshold
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Improved upper bounds for 3-SAT
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A sharp threshold in proof complexity yields lower bounds for satisfiability search
Journal of Computer and System Sciences - STOC 2001
Annals of Mathematics and Artificial Intelligence
Toward a Model for Backtracking and Dynamic Programming
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Lower bounds for k-DNF resolution on random 3-CNFs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Exponential lower bounds and integrality gaps for tree-like Lovász-Schrijver procedures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Further investigations into regular XORSAT
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Note: On exponential time lower bound of Knapsack under backtracking
Theoretical Computer Science
The complexity of inversion of explicit goldreich's function by DPLL algorithms
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Lower bounds for myopic DPLL algorithms with a cut heuristic
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Pseudorandom generators with long stretch and low locality from random local one-way functions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
Robust pseudorandom generators
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Theory of Computing Systems
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DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satisfiability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatisfiable formulas are equivalent to treelike resolution proofs. Therefore, lower bounds for treelike resolution (known since the 1960s) apply to them. However, these lower bounds say nothing about the behavior of such algorithms on satisfiable formulas. Proving exponential lower bounds for them in the most general setting is impossible without proving P 驴 NP; therefore, to prove lower bounds, one has to restrict the power of branching heuristics. In this paper, we give exponential lower bounds for two families of DPLL algorithms: generalized myopic algorithms, which read up to n 1驴驴 of clauses at each step and see the remaining part of the formula without negations, and drunk algorithms, which choose a variable using any complicated rule and then pick its value at random.