Computer Science: An Overview (13th Edition) (What's New in Computer Science)
13th Edition
ISBN: 9780134875460
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Question
Chapter 12.2, Problem 1QE
Program Plan Intro
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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The state transition diagram for a Turing machine that performs unary increment is shown below.
FIGURE 12.6
1/1/R
State 1
6/1/R
State 2
State diagram for the incrementer
Show how this Turing machine will process the input "1111111". You are required to show the configuration of the Turing machine at the
beginning of the execution and after each execution step until the Turing machine halts.
draw
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}*}
Chapter 12 Solutions
Computer Science: An Overview (13th Edition) (What's New in Computer Science)
Ch. 12.1 - Prob. 1QECh. 12.1 - Prob. 2QECh. 12.1 - Prob. 3QECh. 12.1 - Prob. 4QECh. 12.2 - Prob. 1QECh. 12.2 - Prob. 2QECh. 12.2 - Prob. 3QECh. 12.2 - Prob. 4QECh. 12.2 - Prob. 5QECh. 12.3 - Prob. 1QE
Ch. 12.3 - Prob. 3QECh. 12.3 - Prob. 5QECh. 12.3 - Prob. 6QECh. 12.4 - Prob. 1QECh. 12.4 - Prob. 2QECh. 12.4 - Prob. 3QECh. 12.5 - Prob. 1QECh. 12.5 - Prob. 2QECh. 12.5 - Prob. 4QECh. 12.5 - Prob. 5QECh. 12.6 - Prob. 1QECh. 12.6 - Prob. 2QECh. 12.6 - Prob. 3QECh. 12.6 - Prob. 4QECh. 12 - Prob. 1CRPCh. 12 - Prob. 2CRPCh. 12 - Prob. 3CRPCh. 12 - In each of the following cases, write a program...Ch. 12 - Prob. 5CRPCh. 12 - Describe the function computed by the following...Ch. 12 - Describe the function computed by the following...Ch. 12 - Write a Bare Bones program that computes the...Ch. 12 - Prob. 9CRPCh. 12 - In this chapter we saw how the statement copy...Ch. 12 - Prob. 11CRPCh. 12 - Prob. 12CRPCh. 12 - Prob. 13CRPCh. 12 - Prob. 14CRPCh. 12 - Prob. 15CRPCh. 12 - Prob. 16CRPCh. 12 - Prob. 17CRPCh. 12 - Prob. 18CRPCh. 12 - Prob. 19CRPCh. 12 - Analyze the validity of the following pair of...Ch. 12 - Analyze the validity of the statement The cook on...Ch. 12 - Suppose you were in a country where each person...Ch. 12 - Prob. 23CRPCh. 12 - Prob. 24CRPCh. 12 - Suppose you needed to find out if anyone in a...Ch. 12 - Prob. 26CRPCh. 12 - Prob. 27CRPCh. 12 - Prob. 28CRPCh. 12 - Prob. 29CRPCh. 12 - Prob. 30CRPCh. 12 - Prob. 31CRPCh. 12 - Suppose a lottery is based on correctly picking...Ch. 12 - Is the following algorithm deterministic? Explain...Ch. 12 - Prob. 34CRPCh. 12 - Prob. 35CRPCh. 12 - Does the following algorithm have a polynomial or...Ch. 12 - Prob. 37CRPCh. 12 - Summarize the distinction between stating that a...Ch. 12 - Prob. 39CRPCh. 12 - Prob. 40CRPCh. 12 - Prob. 41CRPCh. 12 - Prob. 42CRPCh. 12 - Prob. 43CRPCh. 12 - Prob. 44CRPCh. 12 - Prob. 46CRPCh. 12 - Prob. 48CRPCh. 12 - Prob. 49CRPCh. 12 - Prob. 50CRPCh. 12 - Prob. 51CRPCh. 12 - Prob. 52CRPCh. 12 - Prob. 1SICh. 12 - Prob. 2SICh. 12 - Prob. 3SICh. 12 - Prob. 4SICh. 12 - Prob. 5SICh. 12 - Prob. 6SICh. 12 - Prob. 7SICh. 12 - Prob. 8SI
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- 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.arrow_forwardQuestion 1 A Turing Machine is defined by the following 5 tuples: (0,0,1,0,R) (0,1,1,1,L) (0,b,b,O,L) (1,0,0,1,L) (1,1,0,1,R) The initial configuration is shown below: b 0 0 1 1 1 b 0 Select the correct statements below: There is no 'O' on the tape when the machine halts. Rule (0,1,1,1,L) is never applied. Rule (1,0,0,1,L) is never applied. This Turing Machine will halt.arrow_forwardDesign 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…arrow_forward
- The Church-Turing thesis tells us that Choose one: a.A mechanical device can be intelligent. b.A mechanical device can process mathematical deduction. c.A computer cannot have a soul.arrow_forward4. Give a formal state diagram of a Turing Machine which recognizes the language {#a" + am : n+m = a' : n, m E N}. (You can use the "#" symbol to recognize the beginning of the tape.) SOLUTION:arrow_forwardExplain the formal description of a Turing Machine in clear and short words by describing each component of the formal description.arrow_forward
- Design a Turing machine that multiplies any +ve number by four. So if tape contains the number 5 (in its binary form) then TM should leave 20 on the tape (in binary form). Basically you need to implement this function: Y = 4Xarrow_forwardPlease help With clear explanationarrow_forwardDesign a Turing machine that accepts a string of a and b where the number of a's is one more than the number of of b's? first write the outline then the draw the diagram.arrow_forward
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