1. Consider the following language in the alphabet E = {a}. L = {a²" |n a non-negative integer } Here is a multi-step implementation level description of a Turing machine that decides this language. BobOn input string w: 1. If the tape contains a single a, accept. 2. If the tape contains more than a single a and the number of a's is odd, reject. 3. Sweep left to right across the tape, crossing off every other a 4. Return the head to the left-hand end of the tape and goto step 1 Fill in the following table for Bob, when it is processing a string w of length n. Stage # Max. number of steps to execute Max. number of times executed Order (like O(?)) 1 n 2 3 4 Write a paragraph analyzing the time complexity of Bob. Does Bob show that I a member of P? Why or why not?

Write a Java program to take a string and a non-negative int n, þrint a larger string that is n copies of the original string.

Design a java program with an algorithm that will take a string from the user and then decide if each character in that string is unique. For example, if you ask the user to enter a string and that user enters the world ‘hello’, the result of the algorithm implementedshould return ‘false’ or ‘not unique’. If the user enters a string such as the word ‘phone’ the program will return ‘true’ or ‘unique’ since every character in the word phone is unique and is not repeated. An example of this program follows: Output should show as :  enter a string rizma This string has all the unique characters  would u like to continue?(y for yes n for no) y Enter a string waali This string is not unique

Q2. Construct regular expressions for the following languages. Verify your answer by generating at least one correct string. a. The language over the alphabet (a, b, c) of all three letter words that end in bc b. The language over the alphabet (a, b, c}of all words starting with any number of a's, followed by any number of b's and ending in one or two c's c. The language over the alphabet (a, b, c, d, e, f} where each string starts with a "ab", has either c or d in the middle, and ends with any number of the substring "ef". d. The language over the alphabet (a, b, c) of all words where the words start with either an a or a b followed by as many c's as we want. (the total number or a or b cannot be more that 1) (in any string ther can only be one a or one b) e. The language of only those strings over A= {0, 1} which have exactly 2 zeros