In 1986, Babai, Frankl and Simon (BFS86) defined the polynomial hierarchy in communication complexity and asked whether Σ ee 2 = Φ ee 2 . In order to tackle this problem, researchers have looked at an infinite version. We recently became aware of a paper from 1979 where Miller Mil79 shows that this infinite version is independent of the axioms of set theory. In this note we will describe Miller's result and give a simplified proof of one direction by showing that the continuum hypothesis implies that Σ r 2 = Φ r 2 p (R × R).
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The infinite version of an open communication complexity problem is independent of the axioms of set theory
Fortnow, Lance; Kurtz, Stuart; Whang, Duke
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, Volume 25 (1)
Association for Computing Machinery – Mar 1, 1994
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