Abstract
We present a reduction from the Pigeon-Hole Principle to the classical Sperner Lemma. The reduction is used
1. to show that the Sperner Lemma does not have a short constant-depth Frege proof, and
2. to prove lower bounds on the Query Complexity of the Sperner Lemma in the Black-Box model of Computation.
This research was funded by EPSRC under grant EP/C526120/1.
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Dantchev, S. (2006). On the Complexity of the Sperner Lemma. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_12
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DOI: https://doi.org/10.1007/11780342_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35466-6
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