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hw_06 - Problem Set 6 Fall 09 Due No due date these are...

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Unformatted text preview: Problem Set 6 Fall 09 Due: No due date! these are practice problems. Please follow the homework format guidelines posted on the class web page: http://www.cs.uiuc.edu/class/fa09/cs373/ 1. [ Points: ??] Prove that this language is P -complete: machine L = { M, x, 0k | Turing 2. [ M accepts string x in at most k steps} Points: Points: ??] Show that if 3. [ ??] A is a language in NP, then A∗ is a language in NP. Show that if A is a language in P, then A∗ is a language in P (try to design an algorithm similar to CYK for this problem). 4. [ Points: ??] Prove that computing a long path in a given graph is following language is NP-complete. More specically, prove that the NP-complete: L = { G, k | graph G has a path of length at least k} (Try to reduce some known NP-complete language to L). 1 ...
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