Unformatted text preview: CS 151 Complexity Theory Spring 2011 Midterm Out: April 28 Due: May 5 at the beginning of class This is a midterm. You may consult any of the course materials and the text (Papadimitriou), but not any other source or person. Please attempt all problems, and write clear, concise solutions. Good luck! To facilitate grading, please turn in each problem on a separate sheet of paper and put your name on each sheet. Do not staple the separate sheets. 1. Show that coNEXP ⊆ NEXP / ( n +1). Here the “ / ( n +1)” means that the nondeterministic machine takes exactly ( n +1) bits of advice on an input of length n . Hint: use an idea similar to one you used for problem 2 on Problem Set 2. 2. A branching program is a directed acyclic graph with three distinguished nodes, called start , accept , and reject . Every node except accept and reject is labeled by a positive integer i , and has exactly two outgoing edges, one labeled “0” and the other labeled “1”. An input x = x 1 x 2 . . . x....
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 Fall '09
 Computational complexity theory, Boolean function, Boolean satisfiability problem, Binary decision diagram, Propositional directed acyclic graph

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