Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
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)
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)
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
Optimality of size-width tradeoffs for resolution
Computational Complexity
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A Switching Lemma for Small Restrictions and Lower Bounds for k-DNF Resolution
SIAM Journal on Computing
Parameterized Proof Complexity
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The Resolution Complexity of Independent Sets and Vertex Covers in Random Graphs
Computational Complexity
On the constant-depth complexity of k-clique
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Resolution Is Not Automatizable Unless W[P] Is Tractable
SIAM Journal on Computing
k-Subgraph Isomorphism on AC0 Circuits
Computational Complexity - Selected papers from the 24th Annual IEEE Conference on Computational Complexity (CCC 2009)
Information Processing Letters
The Monotone Complexity of k-clique on Random Graphs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Parameterized bounded-depth Frege is not optimal
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Clique problem, cutting plane proofs and communication complexity
Information Processing Letters
Parameterized Bounded-Depth Frege Is not Optimal
ACM Transactions on Computation Theory (TOCT)
Parameterized Complexity of DPLL Search Procedures
ACM Transactions on Computational Logic (TOCL)
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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 Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the running time of parameterized DPLL procedures. We illustrate this technique by showing lower bounds to the parameterized pigeonhole principle and to the ordering principle. As our main application we study the DPLL procedure for the problem of deciding whether a graph has a small clique. We show that proving the absence of a k-clique requires nO(k) steps for a non-trivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked in [11] of understanding the Resolution complexity of this family of formulas.