On Toda's Theorem in Structural Communication Complexity
نویسنده
چکیده
We prove Toda's Theorem in the context of structural communication complexity, i.e. PH ⊆ BP · ⊕P ⊆ P(#P) = P(PP). The class PSPACE was de ned via alternating protocols with O(log n) many alternations. We consider the class BP · ⊕P of Toda's Theorem, and show that every language in this class can be decided with alternating protocols using O(log n/ log log n) many alternations. The proof is based on a new alternating protocol for the inner product function IP with O(log n/ log log n) many alternations.
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