We showed the reduction from 3-SAT to INDEPENDENT SET in class. Given the following graph G,the correct statements are:-DU-A-B-CG corresponds to a 3-SAT formula (A V BV C) A (D VEVA) A (AVDV C).OG corresponds to a 3-SAT formula (A A BAC) V (DAEAA) V (AADA C).OG corresponds to a 3-SAT formula (A V¬BV C) A (-DVEVA) A (¬AV DV¬C).OG corresponds to a 3-SAT formula (AA¬BAC) V (DAEAA) V (¬AADA ¬C).

A 3-SAT formula can be defined in such a way that it is a Boolean formula wherein every clause…

Answered: We showed the reduction from 3-SAT to…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Mathematical Logic First-order or predicate logic. Show that the sum relation, {(m,n,p)|p=m+n}, is not definable on (N; ∙). Hint: Consider an automorphism of (N; ∙) that interchanges two primes. Where N is the set of natural numbers. Please be as clear as possible. Show and explain all the steps. Thank you very much.
Exercise c. Strict matchingConsider the following generalization of the maximum matching problem, which we callStrict-Matching. Recall that a matching in an undirected graph G = (V, E) is a setof edges such that no distinct pair of edges {a, b} and {c, d} have endpoints that areequal: {a, b} ∩ {c, d} = ∅. Say that a strict matching is matching with the propertythat no pair of distinct edges have endpoints that are connected by an edge: {a, c} ̸∈ E,{a, d} ̸∈ E, {b, c} ̸∈ E, and {b, d} ̸∈ E. (Since a strict matching is also a matching, wealso require {a, b} ∩ {c, d} = ∅.) The problem Strict-Matching is then given a graphG and an integer k, does G contain a strict matching with at least k edges.Prove that Strict-Matching is NP-complete.
Find the lowest common ancestor (LCA) of v and w given a DAG and two vertices, v and w. The LCA of v and w is a v and w ancestor who has no v and w ancestors who are also ancestors of v and w. Finding the degree of inbreeding in a pedigree graph and other applications involving genealogical data analysis and multiple inheritance in computer languages both benefit from computing the LCA. Hint: In a DAG, define the height of a vertex as the distance along the longest path from a root to the vertex. The tallest vertex among those that are both v and w's ancestors is an LCA of v and w.
Prove that the following languages are not regular using the Pumping lemma and/or closure properties. Note: Do not use other methods. a. L1 = {w ∈ {a, b}∗: na(w) + nb(w) = 3 · nb(w)} (na (w) is used to denote the number of a's in the string w) b. L2 = {anbmck: n, m, k ∈ ℕ, n < m or n < k}
Problem 1. Consider the regular expression (0|1)*1 over the alphabet {0, 1} What language does the regular expression describe? Use the Thompson's construction method to derive a non-deterministic finite automaton (NFA) that recognizes L. It is enough to draw the final NFA Use the powerset construction method to derive an equivalent deterministic finite automaton (DFA). You must show the computation of e-closures and draw the DFA Use the partitioning method to derive an equivalent, minimal DFA. You must show the partitioning steps and draw the minimal DFA
Design a deterministic finite-state automaton over the alphabet {a; b; c}that accepts words where each character is immediately followed by atleast one identical character. For example, it accepts the wordsY(gamma sigh), aa, aaa,aabbbbaacc, but it rejects the words a, baba, cbbba. Write the transition function of the automaton as a table and draw the automaton in the form of a transition diagram. Try to design the simplest possible automaton, i.e., an automaton with the smallest number of states.

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