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# hw_template - f P → N with the property that ∃ n ∈ N...

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CS 151 Complexity Theory Spring 2011 Sample L A T E X Template March 27, 2011 (Your Name) 1. Please remember that homework solutions should be: Clear Concise Precise Legible (if handwritten). 2. An example 1 : (Yes) “According to the ‘fundamental theorem of arithmetic’ (proved in ex. 1.2.4-21), each positive integer u can be expressed in the form u = 2 u 2 3 u 3 5 u 5 7 u 7 11 u 11 . . . = p p prime p u p where the exponents u 2 , u 3 , . . . are uniquely determined nonnegative integers, and where all but a Fnite number of the exponents are zero.” (No) “If L + ( P, N 0 ) is the set of functions

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Unformatted text preview: f : P → N with the property that ∃ n ∈ N ∀ p ∈ P p ≥ n ⇒ f ( p ) = 0 then there exists a bijection N 1 → L + ( P, N ) such that if n → f then n = p p ∈ P p f ( p ) . Here P is the prime numbers and N 1 = N ∼ { } .” 3. Show that P = NP . (a) If N = 1 then P = P . (b) If P = 0 then 0 = 0. (c) Collect \$1 million. 1 Taken from Mathematical Writing by Knuth, Larrabee, and Roberts. 1 4. This page intentionally left blank. 2...
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hw_template - f P → N with the property that ∃ n ∈ N...

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