review3 - φ has exactly one True literal Show that...

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Computer Science 340 Reasoning about Computation Review Session 3 Monday, January 14, 2008 Problem 1 An algebraic number is a complex number that is a root of a polynomial with integer coefficients. Is the set of algebraic numbers countable ? Problem 2 A useless state in a Turing Machine is one that is never entered on any input string. Consider the problem of testing whether a Turing machine has any useless states. Formulate this problem as a language and show that it is undecidable. Problem 3 In the Exactly-one 3SAT problem, we are given a 3CNF formula φ , and need to decide if there exists a satisfying assignment such that every clause of
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Unformatted text preview: φ has exactly one True literal. Show that Exactly-one 3SAT is NP-complete. Problem 4 In the MAX CUT problem, we are given an undirected graph G , an integer K and have to decide where there is a subset of vertices S such that there are at least K edges that have one endpoint in S and one endpoint in S . Prove that this problem is NP-complete by giving a reduction from the following variant of 3SAT which is known to be NP-complete: In the Not-All-Equal SAT problem, we are given a 3CNF formula φ and need to decide if there exists a satisfying assignment such that every clause of φ has one or two True literals....
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