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)
Information and Computation
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
Resolution and the Weak Pigeonhole Principle
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
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 combinatorial characterization of treelike resolution space
Information Processing Letters
A Switching Lemma for Small Restrictions and Lower Bounds for k-DNF Resolution
SIAM Journal on Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
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 Proof Complexity
Computational Complexity
Clause-learning algorithms with many restarts and bounded-width resolution
Journal of Artificial Intelligence Research
Parameterized complexity of DPLL search procedures
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Parameterized Bounded-Depth Frege Is not Optimal
ACM Transactions on Computation Theory (TOCT)
Parameterized Complexity
Hi-index | 0.00 |
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 that 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 nΩ(k) steps for a nontrivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked by Beyersdorff et al. [2012] of understanding the Resolution complexity of this family of formulas.