Home15Complexity

# Home15Complexity - CS 341 Automata Theory Elaine Rich...

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CS 341 Automata Theory Elaine Rich Homework 15 Due Friday, Dec. 8 at 11:55 pm 1) Let M be an arbitrary Turing machine. a) Suppose that timereq ( M ) = 3 n 3 ( n +5)( n -4). Circle all of the following statements that are true: i) timereq ( M ) O ( n ). ii) timereq ( M ) O ( n 6 ). iii) timereq ( M ) O ( n 5 /50). iv) timereq ( M ) Θ ( n 6 ). b) Suppose that timereq ( M ) = 5 n 3 n 3 . Circle all of the following statements that are true: i) timereq ( M ) O ( n 5 ). ii) timereq ( M ) O (2 n ). iii) timereq ( M ) O ( n !). 2) Consider the language NONEULERIAN = {< G > : G is an undirected graph and G does not contain an Eulerian circuit}. a) Show an example of a connected graph with 8 vertices that is in NONEULERIAN. b) Prove that NONEULERIAN is in P. 3) Prove that SUBSET-SUM = {< S , k > : S is a multiset (i.e., duplicates are allowed) of integers, k is an integer, and there exists some subset of S whose elements sum to k } is in NP.

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## This note was uploaded on 12/03/2009 for the course CS 341 taught by Professor Rich during the Fall '08 term at University of Texas at Austin.

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Home15Complexity - CS 341 Automata Theory Elaine Rich...

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