Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lower Bound Methods for Tree-like Cutting Plane Proofs   In the book Boolean Function Complexity by Stasys Jukna, two lower bound
techniques for Tree-like Cutting Plane proofs (henceforth, "Tree-CP proofs")
using Karchmer-Widgerson type communication games (henceforth, "KW games") are
presented: The first, applicable to Tree-CP proofs with bounded coefficients,
translates Omega(t) deterministic lower bounds on KW games to 2^Omega(t/log n)
lower bounds on Tree-CP proof size. The second, applicable to Tree-CP proofs
with unbounded coefficients, translates Omega(t) randomized lower bounds on KW
games to 2^Omega(t/log^2 n) lower bounds on Tree-CP proof size.
  The textbook proof in the latter case uses a O(log^2 n)-bit randomized
protocol for the GreaterThan function. However, Nisan mentioned using the ideas
of Feige, et al. to construct a O(log n + log(1/epsilon))-bit randomized
protocol for GreaterThan. Nisan did not explicitly give the proof, though later
results in his paper assume such a protocol.
  In this short exposition, we present the full O(log n + log(1/epsilon))-bit
randomized protocol for the GreaterThan function based on the ideas of Feige,
et al. for "noisy binary search." As an application, we show how to translate
Omega(t) randomized lower bounds on KW games to 2^Omega(t/log n) lower bounds
on Tree-CP proof size in the unbounded coefficient case. This equates
randomness with coefficient size for the Tree-CP/KW game lower bound method.
  We believe that, while the O(log n + log(1/epsilon))-bit randomized protocol
for GreaterThan is a "known" result, the explicit connection to Tree-CP proof
size lower bounds given here is new.

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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin