This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CSci 5403, Spring 2010 Stefan NelsonLindall Homework 2 Example Solution 1. Games. Prove that the following problems are PSPACEcomplete: (a) A Stochastic Satisfiability instance is a quantified boolean formula, only the universal quantifier is replaced by the random R quantifier (meaning, for a random x). An instance x 1 R x 2 x 3 . .. Q n x n is in ssat if x 1 R x 2 x 3 . .. Q n x n Pr[ ( x 1 , .. . ,x n )] 1 2 . Show that ssat is PSPACEcomplete. In some sense, ssat is a game against nature, e.g. we can think of the player in a formula game instance playing against an opponent who is not explicitly adversarial, but simply moves randomly at each stage. It might seem like this should be an easier game to win, but your reduction shows this is not always true. Pf: ssat is PSPACEhard Reduction from fg . Map the formula game instance f = Q 1 x 1 . .. Q i x i ( x 1 , .. . x i ) to the ssat problem f = R x Q 1 x 1 ... Q i x i ( x ( x 1 , .. . x i )) where Q k = if Q k is R if Q k is . x will be assigned 1 with probability 1 2 , and Pr[ x ] = Pr[ x ] Pr[ ]. If f fg , then for any possible assignment of random variables the resulting formula is satisfiable, so Pr[ ] = 1, Pr[ x ] = 1 2 , and hence f ssat . If f fg , then there exists some assignment of random variables such that the resulting formula is not satisfiable. This makes Pr[ ] < 1, so Pr[ x ] < 1 2 , and hence f ssat ....
View
Full
Document
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.
 Spring '08
 Sturtivant,C

Click to edit the document details