Unformatted text preview: 2. A boolean formula is in disjunctive normal form (DNF) if it is a disjunctions (OR) of several clauses, each of which is the conjunction (AND) of several literals, each of which is either a variable or its negation. For example: ( a ∧ b ∧ c ) ∨ ( ¯ a ∧ b ) ∨ ( ¯ c ∧ x ) Given a DNF formula give a polynomial algorithm to check whether it is satisﬁable or not. Why this does not imply P = N P . 3. Prove that the following problems are NP-complete. (a) Given an undirected graph G , does G have a spanning tree in which every node has degree at most 17? (b) Given an undirected graph G , does G have a spanning tree with at most 42 leaves? 1...
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This note was uploaded on 01/22/2012 for the course CS 573 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08