assign4

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

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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
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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...
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