On the Automatizability of Resolution and Related Propositional Proof Systems
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Information Processing Letters
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Abstract: We prove that any optimal tree resolution proof of PHP^m_n is of size 2^{\theta(n log n)}, independently from m, even if it is infinity. So far, only a 2^{\Omega(n)} lower bound has been known, in the general case. We also show that any, not necessarily optimal, regular tree resolution proof PHP^m_n is bounded by 2^{O(n log m)}. To best of our knowledge, this is for the first time, the worst case proof complexity is considered. Finally, we discuss possible connections of our result to Riis' complexity gap theorem for tree resolution.