A Simple Proof of Toda's Theorem
نویسنده
چکیده
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. ACM Classification: F.1.3 AMS Classification: 68Q15
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A S IMPLE P ROOF OF T ODA ’ S T HEOREM Proof of Lemma 1
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. ACM Classifi...
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عنوان ژورنال:
- Theory of Computing
دوره 5 شماره
صفحات -
تاریخ انتشار 2009