Journal of the ACM (JACM)
SIAM Journal on Computing
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Experimental results on the application of satisfiability algorithms to scheduling problems
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Act, and the rest will follow: exploiting determinism in planning as satisfiability
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
On the complexity of choosing the branching literal in DPLL
Artificial Intelligence
On Interpolation and Automatization for Frege Systems
SIAM Journal on Computing
A machine program for theorem-proving
Communications of the ACM
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
SIAM Journal on Computing
Logical Cryptanalysis as a SAT Problem
Journal of Automated Reasoning
Satisfiability, Branch-Width and Tseitin Tautologies
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Complexity of Finding Short Resolution Proofs
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Dependent and Independent Variables in Propositional Satisfiability
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Tuning SAT Checkers for Bounded Model Checking
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Intriactability of Read-Once Resolution
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Resolution is Not Automatizable Unless W[P] is Tractable
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Non-automatizability of bounded-depth frege proofs
Computational Complexity
Automatic SAT-compilation of planning problems
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
The computational complexity of probabilistic planning
Journal of Artificial Intelligence Research
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
From approximate clausal reasoning to problem hardness
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
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DPLL and resolution are two popular methods for solving the problem of propositional satisfiability. Rather than algorithms, they are families of algorithms, as their behavior depends on some choices they face during execution: DPLL depends on the choice of the literal to branch on; resolution depends on the choice of the pair of clauses to resolve at each step. The complexity of making the optimal choice is analyzed in this article. Extending previous results, we prove that choosing the optimal literal to branch on in DPLL is Δp2[log n]-hard, and becomes NPPP-hard if branching is only allowed on a subset of variables. Optimal choice in regular resolution is both NP-hard and coNP-hard. The problem of determining the size of the optimal proofs is also analyzed: it is coNP-hard for DPLL, and Δp2[log n]-hard if a conjecture we make is true. This problem is coNP-hard for regular resolution.