Volume 5 (2009) Article 7 pp. 135-140 [Note]
A Simple Proof of Toda's Theorem
Received: January 21, 2009
Published: July 3, 2009
Keywords: Toda's Theorem, relativization
ACM Classification: F.1.3
AMS Classification: 68Q15

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 BPPP. 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.