Computer Science: An Overview (12th Edition)
12th Edition
ISBN: 9780133760064
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Chapter 12, Problem 14CRP
Program Plan Intro
Turing machine:
Turing machine is used as a tool to understand the power of
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(b) Suppose that you were asked to design a
Turing machine that, when started scan-
ning a square on a completely blank tape,
writes the string ababbaab on the tape
and halts scanning the leftmost symbol of
this string. What is the minimal number
of states required in order to accomplish
this?
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.
Problem 4 Turing Machines
Construct a Turing machine that recognizes the set of all bit strings that contain at least two l's. You
need to define the state transition table in the format used in lectures. That is, f(s;, a) = (s;, A, R)
where s; is the current state, s; is the next state, a is the input symbol, A is the output symbol
written on tape, and L indicates moving left or R indicates moving right.
Chapter 12 Solutions
Computer Science: An Overview (12th Edition)
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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- Given a transition graph of a Turing machine. (a) Write a program for the Turing Machine Simulator based on the given transition graph. (b) Test (at least one time) your program (a) on the Turing Machine Simulator. Give the screen images: - before the work of TMS - after the work of TMS (c) What the given Turing machine computes? (d) In how many steps the given Turing machine processes the input data of the length n?arrow_forwardplease drawarrow_forwardBuild a turing machine with three tracks that add two binary numbers. Considerate the data is stored in the first two tracks and aligned to the right. The result would be written to the third track which is initially empty. Make the ilustration of the turing machine and please explain all steps of the solution.arrow_forward
- Work shown would be very much appreciated. (Only need number 1)arrow_forwardBuild a Turing Machine T.M with three tracks that add two binary numbers. We will consider that the datas are stored in the first two tracks and are aligned to the right. The result will be written to the third track which is initially empty.arrow_forwardFor a Turing machine M, (M) refers to the binary representation of M. For a Turing machine M, L(M) contains the set of all strings accepted by M. For a Turing machine M and an input x = {0,1}*, Steps(M, x) refers to the number of steps taken by M to execute on x before it halts. Here, one step of execution of M on x = one movement (left or right) of the tape head. For a Turing machine M and an input x = {0,1}*, we define the following: ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x} Informally, it contains all locations on the tape that are visited when M is ecuted on x. The leftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and so on. A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, if w₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elements such that π(w₁) = W2.arrow_forward
- 5. Write a Turing machine that computes the function f (n)=n mod3. You may submit a state-transition diagram or the delta-function definition.arrow_forwardCould you assist me with this question? I'm finding it challenging and would appreciate a step-by-step explanation.question that I really need help with:5.13 A useless state in a Turing machine is one that is never entered on any input string. Consider the problem of determining whether a Turing machine has any useless states. Formulate this problem as a language and show that it is undecidable.arrow_forwardA common problem that arises in software maintenance is identifying (and then removing) dead code, code that will never be executed no matter what input the program is given. The analogous problem for TMs would be to determine if a state is never entered, no matter what input the TM is given. Prove by reduction that Ldead, the set of pairs (T,s) where T is a Turing machine and s is a dead state, is not recursive.arrow_forward
- Build a Turing Machine T.M. with three tracks that receives two binary numbers and indicates which of the two is higher. We will consider that the data are stored in the first two tracks and aligned to the right, it means, the least significant bits of both are located in the same column. In the third track it will be written a B, a L or an E, indicating respectively that the first number is larger, smaller or equal to the second.arrow_forward4. Draw the Turing machine that computes the function f(x,y) = x+2y, with both x and y strictly positive integers.arrow_forwardGive the transition diagram for a Turing machine to compute the function f(x) = x + 3, where x is an integer expressed in unary notation. If you would like to assume that there is a special symbol such as $ on the left hand side of the tape, that is fine. Keep in mind that the Turing machine should end with the read/write head on the first symbol of the output, and there should be nothing on the tape except the output (and the $ symbol if you use it).arrow_forward
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