Given a 3-CNF formula and number k find if there exists a satisfying assignment such that at least k variables are FALSE. Is this problem NP-complete or not? Why?
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Given a 3-CNF formula and number k find if there exists a satisfying assignment such that at least k
variables are FALSE. Is this problem NP-complete or not? Why?
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- Long chain of friends: You are given a list of people, and statements of the form “x knows y”. You are asked to find, is there a chain of k distinct people, such as x1 knows x2, x2 knows x3, and xk-1 knows xk. Prove that this problem is NP-complete by using one of the known NP-complete problems (CLIQUE, 3-SAT, Hamiltonian Path, Hamiltonian Cycle, Independent Set, etc.)Show that the following problem belongs to NP class: we are given a set S of integer numbers and an integer number t. Does S have a subset such that sum of its elements is t? Note: Data Structures and Algorithm problemINPUT: A graph G, a non-negative integer k ≥ 0, and a boolean formula F in CNF. OUTPUT: “Yes” if and only if either G has an independent set of size k or if the boolean formula F is satisfiable. Prove that this problem is NP-Complete.
- Show that L= {(@) | q is a Boolean formula with at least 2 satisfying assignments} is NP-hard.Show that the 3-CNF satisfiability problem (3-CNF SAT ) is NP-complete.2. Can someone help with this problem Prove that the following problem is NP-hard and determine whether it is also NP-complete or not – if the problem is NP-complete, you also need to give a poly-time verifier and argue the correctness of your verifier.
- A graduate student is working on a problem X. After working on it for several days she is unable to find a polynomial-time solution to the problem. Therefore, she attempts to prove that he problem is NP-complete. To prove that X is NP-complete she first designs a decision version of the problem. She then proves that the decision version is in NP. Next, she chooses SUBSET-SUM, a well-known NP-complete problem and reduces her problem to SUBSET-SUM (i.e., she proves X £p SUBSET-SUM). Is her approach correct? Explain your answer.In this group of problems, you are given the predicate P(x), where the domain of x is the set of natural numbers.L = {f in SAT | the number of satisfying assignments of f > 1/2 |f| } Show that L is NP-complete