Archive for Mathematical Logic

, Volume 43, Issue 3, pp 351–357 | Cite as

Matrix identities and the pigeonhole principle

Article

Abstract.

We show that short bounded-depth Frege proofs of matrix identities, such as PQ=IQP=I (over the field of two elements), imply short bounded-depth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential-size bounded-depth Frege proofs, it follows that the propositional version of the matrix principle also requires bounded-depth Frege proofs of exponential size.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of Computing and SoftwareMcMaster UniversityCanada
  2. 2.Department of PhilosophyUniversity of TorontoCanada

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