Turing machine: Turing machine is used as a tool to understand the power of algorithmic processes. It consists of a control unit which is used to read and write symbols on a tape. A tape is divided into cells and each cell has one of finite sets of symbols.

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Chapter 12.2, Problem 1QE

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Turing machine:

Turing machine is used as a tool to understand the power of algorithmic processes.

It consists of a control unit which is used to read and write symbols on a tape.

A tape is divided into cells and each cell has one of finite sets of symbols.

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3. Consider the following Turing Machines. Match then with the tickie definition of the language. Write your answer in the blank column of the table below: x/x R a/a R b/b R A/AL a/a L b/b L a/A R b/BR B/BL #/#L a/A L b/BL #/#R 9₂ 4₂ x/x R 40 a/a R b/b R X/X R A/AL B/B L 95 #/#R Y 96 A/a L/ B/b L b/B R 9, 9₂ B/#L 96 #/# R 90 4₂ b/# R #/#L 99 #/#L a/AR A/AR 98 B/BR A/#L a/a L b/b L #/#L a/# R A/AR B/BR a/a R b/b R X/X R a/a R b/b R 9₁ #/# R 9₁ B/BL #/# L 92 9₁ a/# L a/a L 9₂ B/BL #/# L 94 95 b/b L a/a R b/# L b/b R A. L = {w#w | w = {a,b}*} B. L = {www = {a,b}*} 90 B/B R a/a R b/b R a/x R 9, b/x R B/BL #/#R 94 a/x R #/#R x/x R a/a R b/b R x/xR #/#R_ a/a R. b/b R S 92 B/BR 90 91 #/# R. b/x R B/BL 99 95 (910 a/a R b/b R x/x R C. L = ({ww | w = {a, b}*} #/#R 97 b/x L #/#R a/a L b/b L a/a R b/b R 93 96 a/a R b/b R #/#L B/BL 94 x/x L x/x L B/BL a/x L x/x L #/#L a/x L a/a L b/b L x/x R as 9 b/x L 97 D. L = {w#w² | w = {a, b}*}

7. Design a Turing machine that adds two integers together. The number system is as following, O is represented as 1, 1 is represented as 11, 2 is represented as 111, and so on.

Design a Turing machine to compute the x mod y, y>0 function. On entry, the number is represented as a unary number using |. This way, 5 will turn to |||||. When two numbers are inputted, they are placed as unary numbers separated by #. The answer must contain states, with clear instructions on what to do when finding a symbol, namely what state to go to, where to go (Stay, Left, Right) and what symbol to put in a cell. E.g.: q0 If found _, put _, go to q1 and Stay. If found |, put |, go to q0 and Left. q1 If found _, put _, go to q1 and Right If found |, put X, go to q2 and Right. Etc… Feel free to use as many auxiliary symbols as you need. In the end, the program needs to output n '|' symbols without spaces('_') or anything, where n is the result of x mod y. So, the result for input 10 and 7 and output for it would look like this: We input numbers in the machine, and they appear on the Turing machine line like this, every symbol in its cell: Input: ||||||||||#||||||| Once…