hwsol2.3 - w ∈ L Then since for every x ∈ L | x | = | w...

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CSci 5403, Spring 2010 Ivan Brugere Homework 2, write-up Due: Feb 25, 2010 1. Padding your language. Prove that space ( n ) 6 = P . Your proof will not prove that either is included in the other, but rather that P is closed under some property that space ( n ) is not. This can be shown by contradiction. Assume P = space ( n ). Consider an L space ( n 2 ) and let L 0 be the language L padded to quadratic length. This means that L 0 = { w 1 | w | 2 | w
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Unformatted text preview: w ∈ L } . Then, since for every x ∈ L , | x | = | w 1 | w | 2 | > | w | 2 , L ∈ space ( n ). By P = space ( n ) there exists a TM T that decides L in O ( n c ) time, and thus a TM T that decides L in time O ( n 2 c ). So L ∈ P = space ( n ), therefore space ( n 2 ) ⊆ space ( n ), contradicting the Space Hierarchy Theorem. 1...
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