Putting the Hierarchy in P#P
{"Image DocumentName": "Putting the Hierarchy in P#P", "Image ImageDescription": "Toda\u2019s Theorem: PH \uf0cc P#P. Idea of the proof: Characterize PH in terms circuits. a uniformly constructed constant depth circuit with exponential number of \u00c6 and \u00c7 gates. Consider circuits where the exponentially occurring gates are parity (xor) \u00a9 This corresponds to P\u00a9P. \u00a9P the class of functions expressible as the number of accepting paths mod 2 in some NTM. Show how to approximate an \u00c6 and an \u00c7 gate using a \u00a9 gate . This gives PH \uf0cc RP\u00a9P. Show RP\u00a9P \uf0cc P#P. Tool:\uf065-biased probability spaces.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}