hw4 - CSci 5403 Spring 2010 Homework 4 due 1 Randomness...

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CSci 5403, Spring 2010 Homework 4 due: March 23, 2010 1. Randomness does not help in PSPACE . In lecture, it was stated without proof that BPPSPACE = PSPACE . In this problem, we’ll prove an even stronger version of this result. Define the class PPSPACE to be the class of languages A for which there exists a polynomial space PTM M such that x A Pr r [ M ( x ; r ) accepts] 1 / 2. Prove that PPSPACE PSPACE . Thus, a PSPACE machine gains no advantage by having access to random bits. Hint: Start by restricting a PPSPACE machine to always halt in the same number of steps, and choose a convenient number. Modify the space-efficient search procedure from the proof of Savitch’s theorem to count the exact number of accepting paths. You may apply the fact that integer addition is in uniform NC 1 to get around the (big) problem this algorithm encounters. 2. BPL. Recall that language A is in BPL iff there exists a logspace PTM M such that Pr[ M ( x ; r ) = ( x A )] 2 / 3. Prove that
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This note was uploaded on 10/21/2011 for the course CSCI 5403 taught by Professor Sturtivant,c during the Spring '08 term at Minnesota.

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hw4 - CSci 5403 Spring 2010 Homework 4 due 1 Randomness...

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