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.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.Show that the 3-CNF satisfiability problem (3-CNF SAT ) is NP-complete.
- 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.L = {f in SAT | the number of satisfying assignments of f > 1/2 |f| } Show that L is NP-completeP is the set of problems that can be solved in polynomial time. More formally, P is the set of decision problems (e.g. given a graph G, does this graph G contain an odd cycle) for which there exists a polynomial-time algorithm to correctly output the answer to that problem. What is NP? Consider these five options. A. NP is the set of problems that cannot be solved in polynomial time. B. NP is the set of problems whose answer can be found in polynomial time. C. NP is the set of problems whose answer cannot be found in polynomial time. D. NP is the set of problems that can be verified in polynomial time. E. NP is the set of problems that cannot be verified in polynomial time. Determine which option is correct. Answer either A, B, C, D, or E.