hw6(1) - CS 373: Combinatorial Algorithms, Spring 2001

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CS 373: Combinatorial Algorithms, Spring 2001 http://www-courses.cs.uiuc.edu/~cs373 Homework 6 (due Tue. May 1, 2001 at 11:59.99 p.m.) Name: Net ID: Alias: U 3 / 4 1 Name: Net ID: Alias: U 3 / 4 1 Name: Net ID: Alias: U 3 / 4 1 Starting with Homework 1, homeworks may be done in teams of up to three people. Each team turns in just one solution, and every member of a team gets the same grade. Since 1-unit graduate students are required to solve problems that are worth extra credit for other students, 1-unit grad students may not be on the same team as 3/4-unit grad students or undergraduates. Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Please also tell us whether you are an undergraduate, 3/4-unit grad student, or 1-unit grad student by circling U, 3 / 4 , or 1, respectively. Staple this sheet to the top of your homework. Note: You will be held accountable for the appropriate responses for answers (e.g. give models, proofs, analyses, etc). For NP-complete problems you should prove everything rigorously, i.e. for showing that it is in NP, give a description of a certi±cate and a poly time algorithm to verify it, and for showing NP-hardness, you must show that your reduction is polytime (by similarly proving something about the algorithm that does the transformation) and proving both directions of the ‘if and only if’ (a solution of one is a solution of the other) of the many-one reduction. Required Problems 1. Complexity (a) Prove that P co-NP. (b) Show that if NP n = co-NP, then every NP-complete problem is not a member of co-NP. 2. 2-CNF-SAT Prove that deciding satis±ability when all clauses have at most 2 literals is in P.
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hw6(1) - CS 373: Combinatorial Algorithms, Spring 2001

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