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Tree resolution proofs of the weak pigeon-hole principle.

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.

Item Type:Book chapter
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Publisher statement:© 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Date accepted:No date available
Date deposited:01 November 2010
Date of first online publication:June 2001
Date first made open access:No date available

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