{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw8 - CNF 2 is in P b Show that CNF 3 is NP-complete...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 181 — Winter 2006 Problem Set #8 Formal Languages Due March 12, 2008 Problem 8.1. (10 points) Show that P is closed under union, concatenation, and star. Show that if P=NP, then given a graph G and integer k , you can construct in polynomial time a k -clique of G if one exists. (Careful: the NP problem only tells you whether some k -clique exists , it does not give you one!) Problem 8.2. (10 points) You can do this problem after we talk about NP-completeness. Let CNF k = {h φ i | φ is a satisfiable CNF formula where each variable occurs at most k places } . a. Show that
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CNF 2 is in P . b. Show that CNF 3 is NP-complete. Problem 8.3. (10 points) You can do this problem after we talk about NP-completeness on Monday. Let DBLSAT = {h φ i | φ has at least two satisfying assignments } . Show that DBLSAT is NP-complete. A subset of the nodes of a graph G is a dominating set if every other node of G is adjacent to some node in the subset. Let DOMSET = {h G , k i | G has a dominating set with k nodes } Show that DOMSET is NP-complete. For hardness, reduce from VERTEX-COVER ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online