Received: January 21, 2009
Published: July 3, 2009
Abstract: [Plain Text Version]
Toda in his celebrated paper showed that the polynomial-time hierarchy is contained in P#P. We give a short and simple proof of the first half of Toda's theorem that the polynomial-time hierarchy is contained in BPP⊕P. Our proof uses easy consequences of relativizable proofs of results that predate Toda.
For completeness we also include a proof of the second half of Toda's theorem.
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