Many hard examples for resolution
Journal of the ACM (JACM)
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
A Switching Lemma for Small Restrictions and Lower Bounds for k - DNF Resolution
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Lower bounds for the weak Pigeonhole principle and random formulas beyond resolution
Information and Computation
Random CNF's are Hard for the Polynomial Calculus
FOCS '99 Proceedings of the 40th 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
Pseudorandom Generators in Propositional Proof Complexity
SIAM Journal on Computing
Toward a Model for Backtracking and Dynamic Programming
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Exponential Lower Bounds for the Running Time of DPLL Algorithms on Satisfiable Formulas
Journal of Automated Reasoning
Eulogy: Michael (Misha) Alekhnovich 1978-2006
ACM SIGACT News
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
The complexity of the Hajós calculus for planar graphs
Theoretical Computer Science
Improved lower bounds for tree-like resolution over linear inequalities
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Optimality of size-degree tradeoffs for polynomial calculus
ACM Transactions on Computational Logic (TOCL)
On minimal unsatisfiability and time-space trade-offs for k-DNF resolution
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Complexity of semialgebraic proofs with restricted degree of falsity
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
Short Propositional Refutations for Dense Random 3CNF Formulas
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
| Hi-index | 0.00 |
We prove exponential lower bounds for the refutation of a random 3-CNF with linear number of clauses by k-DNF Resolution for k ≤ √ log n ⁄ log log n. For this we design a specially tailored random restrictions that preserve the structure of the input random 3-CNF while mapping every k-DNF with large covering number to 1 with high probability. Next we make use of the switching lemma for small restrictions by Segerlind, Buss and Impagliazzo to prove the lower bound.This work improves the previously known lower bound for Res(2) system on random 3-CNFs by Atserias, Bonet and Esteban and the result of Segerlind, Buss, Impagliazzo stating that random O(k2)-CNF do not possess short Res(k) refutations.