Dantchev, S.. and Riis, S. (2001) 'Tree resolution proofs of the weak pigeon-hole principle.', in 16th Annual IEEE Conference on Computational Complexity, 18-21 June 2001, Chicago, Illinois ; proceedings. New York: IEEE, pp. 69-77.
We prove that any optimal tree resolution proof of PHPn m is of size 2&thetas;(n log n), independently from m, even if it is infinity. So far, only a 2Ω(n) lower bound has been known in the general case. We also show that any, not necessarily optimal, regular tree resolution proof PHPn m is bounded by 2O(n log m). To the best of our knowledge, this is the first time the worst case proof complexity has been considered. Finally, we discuss possible connections of our result to Riis' (1999) complexity gap theorem for tree resolution.
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|Record Created:||09 Jul 2007|
|Last Modified:||01 Nov 2010 15:27|
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