Download presentation

Presentation is loading. Please wait.

Published byFaith Marsh Modified over 4 years ago

1
Advice Coins Scott Aaronson

2
PSPACE/coin: Class of problems solvable by a PSPACE machine that can flip an advice coin (heads with probability p, tails with probability 1-p) as many times as it wants Clear that PSPACE/poly PSPACE/coin Other direction? Could PSPACE/coin=ALL?

3
Hellman-Cover 1970: To distinguish a p=1/2 coin from a p=1/2+ coin with constant bias, you need a probabilistic finite automaton with (1/ ) states I.e. you cant detect a less than 1/exp(n) change in p without more than poly(n) bits to record the statisticsregardless of how many times you flip the coin Seems to answer our question! Except that it doesnt

4
First problem: p could be unbelievably small (1/Ackermann(n)), and info could be stored in log(1/p) Second problem: Hellman-Cover theorem is false for quantum finite automata! I can give a QFA with 2 qubits that distinguishes p=1/2 from p=1/2+ for any >0 So question stands: PSPACE/coin=ALL? BQPSPACE/coin=ALL?

5
Main Result: PSPACE/coin, BQPSPACE/coin are both contained in Something/poly Main Idea: Limiting distribution (or quantum state) of an s-state automaton can be expressed in terms of degree-s rational functions of p. These can oscillate at most s times as p goes from 0 to 1. Need to count and compare roots of real polynomials. If everything is doable in NC, then a PSPACE/poly upper bound follows.

Similar presentations

OK

Happy Birthday Michael !!. Probabilistic & Nondeterministic Finite Automata Avi Wigderson Institute for Advanced Study Very old (1996) joint work with.

Happy Birthday Michael !!. Probabilistic & Nondeterministic Finite Automata Avi Wigderson Institute for Advanced Study Very old (1996) joint work with.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on recycling of waste in korea Ppt on preservation of public property Ppt on soil pollution Ppt on 2d nmr spectroscopy Ppt on relation and function free download Ppt on national education policy 1986 calendar Ppt on monopoly market structure Civil engineering ppt on high performance concrete Ppt on south african culture pictures Ppt on centre of mass