Journal of the ACM (JACM)
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Hard examples for bounded depth frege
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of 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 Beyond Resolution
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On the automatizability of resolution and related propositional proof systems
Information and Computation
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A lower bound is proved for refutations of certain clause sets in a generalization of Resolution that allows cuts on conjunctions of width 2. The hard clauses are the Tseitin graph formulas for a class of logarithmic degree expander graphs. The bound is optimal in the sense that it is truly exponential in the number of variables.