Computer Science 172 - Spring 1999 - Blum - Midterm 1

Computer Science 172 - Spring 1999 - Blum - Midterm 1 -...

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CS 172, Midterm #1, Spring 1999 CS 172, Spring 1999 Midterm #1 Professor Manuel Blum This is a CLOSED BOOK examination. Calculators ARE permitted. Do all your work on the pages of this examination. Problem #1 a) Define the number of steps taken by a NDTM on input x. b) Define the nubmer of steps taken by a NDTM on inputs of length n. Problem #2 Define two (computational) problems p1, p2 to be poly-time equivalent iff it is possible to solve p1 in polynomial time given an algorithm to solve p2 in polynomial time (p1 <= p2), and vice-versa (p2 <= p1). Are the following two problems poly-time equivalent? If so, prove it. If not, explain why not. Decision: <--m--> m Instance: NDTMi, x in {0,1}*, m in unary (ie 1. ....1 = 1 ). Question: Does NDTMi accept x in m steps? ie does there exist a y in {0,1}* s.t. DTMi accepts (y,x) in m steps?
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Unformatted text preview: Optimization: Input: NDTMi, x in {0,1}*, m in unary Output: y in {0,1}* s.t. DTMi accepts (y,x) in m steps, if any (ie if such y exists); "NONE" if there is no such y. Problem #3 Explain what problems if any you encounter in doing the above reductions in the case that m is given in binary instead of unary. file:///C|/Documents%20and%20Settings/Jason%20Raft. ..-%20Spring%201999%20-%20Blum%20-%20Midterm%201.htm (1 of 2)1/27/2007 6:45:49 PM CS 172, Midterm #1, Spring 1999 Posted by HKN (Electrical Engineering and Computer Science Honor Society) University of California at Berkeley If you have any questions about these online exams please contact mailto:[email protected] file:///C|/Documents%20and%20Settings/Jason%20Raft. ..-%20Spring%201999%20-%20Blum%20-%20Midterm%201.htm (2 of 2)1/27/2007 6:45:49 PM...
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This note was uploaded on 05/17/2009 for the course CS 172 taught by Professor Seshia during the Spring '08 term at Berkeley.

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Computer Science 172 - Spring 1999 - Blum - Midterm 1 -...

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