As we have done in the class, provide brief explanations of how to design a Turing machine for the following languages. Don't draw anything, just explain your algorithm in plain English using the Turing tape. L= {w E {0,1} * |w 0"1": n20}
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- Java considers the String data type as non-primitive, because it contains a sequence of characters and hence there is a predefined class called String dedicated to String processing. The String class has a lot of functions and continues to grow. See https://www.tutorialspoint.com/java/java_strings.htm for more on strings. Your task is to then create a java program that when give a sentence will replace the first occurrence of NUST with Namibia University of Science and Technology. Sample run 1: Enter a sentence: Welcome to my NUST. Output: Welcome to my Namibia University of Science and Technology. Sample run 2: Enter a sentence: The nust is a great institution of high learning. Output: The Namibia University of Science and Technology is a great institution of high learning.In-Class Exercise 6 A set of linear equations is given: 10 x₁ + 4x₂ - 2x3 = 26 4x₁ - 8x₂ + x3 = 0 2 2x₁ + x₂ - 5x3 = 40 4 1) Solve the equations by using Gauss-Seidel iterative method. Do it "by hand" (you can use matlab for arithmetic calculations). Start with guessing answer [X1 X2 X3] = [0 0 0] and try at least three iterations. 2) Use power method to find the smallest eigenvalue of the coefficient matrix. (hint: use inverse of coefficient matrix, then apply power method to find largest eigenvalue. Take inverse of that eigenvalue) 3) Find all eigenvalues and their corresponding eigen vectors of the coefficient matrix.For this exercise, you will create several recursive functions in order to get a better understanding of how recursion works. In exercise 2, we will illustrate using recursion for creating art. Create a new project in IntelliJ called Recursion. Add a new Java class called Recursion with a public static main function. You will add several functions to your Recursion class as follows: 1 Write a recursive function int sum(int n) that adds up the numbers from n to 1 and print your result. For example from main do the following: Recursion recursion = new Recursion();System.out.println(recursion.sum(6)); 1.2 Write a recursive function factorial(int n) that calculates the factorial of n. Print out the results. Add your function to your Recursion class. 1.3. Write a recursive function powerOf10(int n) that calculates 10n. 1.4. Write a more general recursive function powerOfN(int x, int p) that calculates the power of xp. Do not use the Math.pow function. 1.5.…
- The union of two sets A and B is a set that contains all the elements that are in A together with all the elements that are in B. The intersection of A and B is the set that contains elements that are in both A and B. The difference of A and B is the set that contains all the elements of A except for those elements that are also in B.Suppose that A and B are variables of type set in Java. The mathematical operations on A and B can be computed using methods from the Set interface. In particular: A.addAll(B) computes the union of A and B; A.retainAll(B) computes the intersection of A and B; and A.removeAll(B) computes the difference of A and B. Write a program that can be used as a "set calculator" for simple operations on sets of non-negative integers. (Negative integers are not allowed.) A set of such integers will be represented as a list of integers, separated by commas and, optionally, spaces and enclosed in square brackets. For example: [1,2,3] or [17, 42, 9, 53,108]. The…Consider the alphabet set Σ = {a b}; Write Regular Expressions for the following definitions. 7. Language of All those words whose length is odd and they contain ab.8. Language of All those words which ends with bb and have odd length.9. Language of All those words which do not end with ba.This is a fill in the Blank question. Students will see an empty textbook to type their answer. In the following, x and y are variables, A and B are constants. Fill in the correct substitution such that each of a(A, x) and a(y, B) will be the same expression (this process is called Unification). SUBST{X/ , y/
- 1. Write a Graph class in Java. This class should represent undirected graphs. You can choose one of the representationsfrom graph exercises, eg object model, sets of nodes and edges, adjacency matrix, or soon, whichever you feel most comfortable with.● Include comments in your Java file to explain how nodes and edges are represented.● Assume that only one edge can exist between two nodes.● Assume that it is possible to have an edge connecting a node to itself, ie that a nodecan be connected to itself via an edge.● Because edges are undirected, an edge between v and w is also one between w and v.● Your constructor method should take one parameter: the number of nodes of thegraph. Add a method to your class: boolean addEdge that takes two parameters, v andw (representing two modes v and w which are connected together by the edgebeing added). If successful, the method should return true. The method should return false when it isunsuccessful, which is in the following cases: the edge is…2. Java considers the String data type as non-primitive, because it contains a sequence of charactersand hence there is a predefined class called String dedicated to String processing. The String classhas a lot of functions and continues to grow. Seehttps://www.tutorialspoint.com/java/java_strings.htm for more on strings. Your task is to then createa java program that when give a sentence will replace the first occurrence of NUST with NamibiaUniversity of Science and Technology.Sample run 1:Enter a sentence: Welcome to my NUST.Output: Welcome to my Namibia University of Science and Technology.Sample run 2:Enter a sentence: The nust is a great institution of high learning.Output: The Namibia University of Science and Technology is a great institution of high learning NB: IN JAVA PROGRAMMING1. Write a Graph class in Java. This class should represent undirected graphs. You can choose one of the representationsfrom graph exercises, eg object model, sets of nodes and edges, adjacency matrix, or soon, whichever you feel most comfortable with.● Include comments in your Java file to explain how nodes and edges are represented.● Assume that only one edge can exist between two nodes.● Assume that it is possible to have an edge connecting a node to itself, ie that a nodecan be connected to itself via an edge.● Because edges are undirected, an edge between v and w is also one between w and v.● Your constructor method should take one parameter: the number of nodes of thegraph. Add a method to your class: boolean addEdge that takes two parameters, v andw (representing two modes v and w which are connected together by the edgebeing added). If successful, the method should return true. The method should return false when it isunsuccessful, which is in the following cases: the edge is…
- Language is C++ Rare Collection. We can make arrays of custom objects just like we’ve done with ints and strings. While it’s possible to make both 1D and 2D arrays of objects (and more), for this assignment we’ll start you out with just one dimensional arrays: directions as follows in the picturesLanguage is C++ The purpose of this project is to test your ability to use files, strings (Strings?), and libraries effectively in program design. A popular past-time is the word search puzzle (if you don't believe me, look in your daily paper and in the news stand in the check-out line at the grocery store). In such a puzzle, a grid of letters is presented which presumably contains words. However, the words are cleverly hidden among the other letters. Their camouflage is aided by them being aligned in many different orientations: horizontal, vertical, diagonal, and sometimes even backwards! The person's goal is to find the words and circle each one. Most often the person is also given a list of the words which should be found: apple hananabs pear mpearoap banana npsgrape grape uleapnbm orange aenuraol agrafnel epanqust bananais located backwards across the top row. appledrops down from the last ain banana. pearis forwards from the first pin apple. grapeis on the line below this.…Determine whether a string is a palindromeA palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces.The specifications for this assignment are: •Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution: Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes StackVector and QueueVector respectively. You already have access to the relevant exception classes and interfaces for the above ADTs. •All of your belong to a Java…