assign4

assign4 - ,...,n k can be partitioned into two disjoint...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 220 Winter 2011, Assignment 4, Due: March 2 (Wednesday) 1. Describe a deterministic polynomial time bounded TM M which, when given the binary representation of a positive integer N , determines whether or not N = m k for some positive integers m 2 and k 2. More precisely, M should accept the language L = { x | x is a binary number with leading bit 1 representing a positive integer N and N = m k for some m 2 and k 2 } in time polynomial in the length of x . It is suFcient to give an informal description of the operation of M . What are the time and space complexities of M ? 2. Show that L = { M | M is a one-way N±A, L ( M ) is in²nite } is in P. 3. Consider the language L = { 1 n 1 # ... #1 n k | k 1 , each n i 1, and n 1
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ,...,n k can be partitioned into two disjoint sets B 1 and B 2 such that the sum of the integers in B 1 = the sum of the integers in B 2 } . Note that L is the unary representation of the partition problem. Show that L is in P. ( Hint : NSPACE(log n) is contained in P.) 4. Show that if NSPACE ( log n ) = DSPACE ( log n ), then NSPACE ( n ) = DSPACE ( n ). (Use the translation/padding technique.) 5. Show that DSPACE ( n 2 log n ) properly contains DSPACE ( n 2 ). 6. Show that for every positive integer k 1, NSPACE ( n k +1 ) properly contains NSPACE ( n k ) 1...
View Full Document

Ask a homework question - tutors are online