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Unformatted text preview: Lofgren CSci 5403— Homework 2 Problem 5 Let s n ) ≥ log n be time constructable. If L ∈ ASPACE s n )), then there is an alternating TM A which decides it using O s n )) space. We describe a deterministic machine D which decides L using 2 s n )) time. Given x , it determines which nodes in the configuration graph of A lead to an accept state. It does this by initializing a 2 s n )) bit array of 0s, one bit for each vertex in the configuration graph. It sets the accept state s) to 1, and then repeatedly considers the transition function of A . Following Definition 5.7 in our text, if C connects to C in the configuration graph, the state of C has an existential label, and the bit for C is a 1, then the bit for C is set to 1. If C connects to C and C , the state of C has a universal label, and the bits of C and C are set to 1, then the bit for C is set to one. It repeatedly checks every transition until no bits are set on some round....
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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.
- Spring '08