Size space tradeoffs for resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Complexity of Resolution with Bounded Conjunctions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On sufficient conditions for unsatisfiability of random formulas
Journal of the ACM (JACM)
A Resolution Calculus with Shared Literals
Fundamenta Informaticae
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A Resolution Calculus with Shared Literals
Fundamenta Informaticae
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Abstract: We study the space complexity of refuting unsatisfiable random k-CNFs in the Resolution proof system. We prove that for any large enough \Delta, with high probability a random k-CNF over n variables and \Delta n clauses requires resolution clause space of \Omega(n \Delta^{1+\epsilon\over k-2-\varepsilon}, for any 0 \sqrt n. This bound is nearly tight. Specifically, we show that with high probability, a random 3-CNF with \Delta n clauses requires treelike refutation size of exp(\Omega(n/\Delta^{1+\epsilon\over 1-\epsilon})), for any 0