Volume 5 (2009) Article 7 pp. 135-140 [Note]
A Simple Proof of Toda's Theorem
Published: July 3, 2009
Toda in his celebrated paper showed that the polynomial-time hierarchy is contained in $\P^\sharpP$. We give a short and simple proof of the first half of Toda's Theorem that the polynomial-time hierarchy is contained in $\BPP^\parityP$. Our proof uses easy consequences of relativizable proofs of results that predate Toda.