TURING MCHINE
Construct a Turing machine transducer that computes the reverse function on (a,b)*.
F(w) = w^R
That is, the function takes as input a string of a's and b's and outputs the reverse of the string.
Homework Answers
Discrete Mathematical Structures Draw a Turing machine that takes a string representing two unary numbers, x...
Discrete Mathematical Structures
Draw a Turing machine that takes a string representing two unary numbers, x and y, separated by a 0, and determines whether x greaterthanorequalto y. For example, the input for x = 3, y = 4 would be 11101111. Use two halt states: one for yes and one for no. Give the trace of your machine in the previous problem processing the strings 11101111 and 11110111. Draw a TM that computes f(w) = w^R where w elementof...
Introduce a Turing machine to decide the languages to follow. You must Algorithmic description, but with...
Introduce a Turing machine to decide the languages to follow. You must Algorithmic description, but with a sufficient level of detail. You can use the variants of the original model of the Turing machine. {w w^R w | where w is a word formed by 0's and 1's} {w ∈ {a, b}∗| w is a palindrome and has the same number of a's and b's}. Please describe which variant of Turing whether it is with a tape or multi tape....
1. Introduce a Turing machine to decide the languages to follow. You must algorithmic description, but...
1. Introduce a Turing machine to decide the languages to follow. You must algorithmic description, but with a sufficient level of detail. You can use the variants of the original model of the Turing machine. a) A = {0^k 1^i0^j| k = i × j}. b) B = {w w^R w | where w is a word formed by 0's and 1's} c) C = {w ∈ {a, b}∗| w is a palindrome and has the same number of a's...
7. (Exercise 8.5.1) Simulating a Turing machine. Here is a description of a Turing machine. The...
7. (Exercise 8.5.1) Simulating a Turing machine. Here is a description of a Turing machine. The input alphabet is {a, b}. The state set is: {90, 91, 92, 93, 94, qacc, Cre; } The transition function is given in the table below: 90 9 42 93 94 a (qı, a, R) (qı, a, R) (q2, a, R) (qace, a, R) (qej, a, R) b (q2, b, R) (qı, b, R) (qı, b, R) (qrej, b, R) (qace, b, R) **...
40 points) Please design a Turing machine T to recognize the union of the languages of two Turing...
40 points) Please design a Turing machine T to recognize the union of the languages of two Turing machines Mi and M2. That is, T accepts an input string w, if and only if either Mi or M2 or both accept string w. Please describe the high-level idea (or algorithm) of your Turing machine T. You do not need to draw the low-level state transition diagram of your Turing machine. Note that the difficulty is that Mi or M2 may...
State diagrams for Turing Machines. Suppose you are given a string w ∈ {0,1}* placed on a Turin...
State diagrams for Turing Machines. Suppose you are given a string w ∈ {0,1}* placed on a Turing Machine tape. Give the state diagram for the Turing Machine required to take the initial string, w, and replace it on the tape with a new string, w′. The new string, w′, is formed by shifting the entire input string one cell to the right. Suppose you are given a string w ∈ {0, 1}* placed on a Turing Machine tape. Give...
Show that the language A = {<M1> | the language accepted by the Turing Machine M1...
Show that the language A = {<M1> | the language
accepted by the Turing Machine M1 is 1*} is
not decidable. Present your proof in the style of the proof of Th.
5.3, which shows below.
PROOF We let R be a TM that decides REGULARTm and construct TM S to decide ATM. Then S works in the following manner. S - "On input (M, w), where M is a TM and w is a string: 1. Construct the following...
Descrete Math Create a turing machine that has a string of n 1s as input and...
Descrete Math Create a turing machine that has a string of n 1s as input and outputs a string of 2n 1s. Showing the steps test your machine on the input 1111.
State diagrams for Turing Machines. Suppose you are given a string w ∈ {a, b}* placed on a Turing...
State diagrams for Turing Machines. Suppose you are given a string w ∈ {a, b}* placed on a Turing Machine tape. Give the state diagram for the Turing Machine recognizing language: L = {w#w##w|w ∈ {a, b}*}.
Turing machine that subtracts two from the input string corresponding a ternary number.
Implement a Turing machine that subtracts two from the input string corresponding a ternary number. More specifically, suppose w = an−1an−2 . . . a1a0 is the input string with ai ∈ {0, 1, 2}. Your Turing machine should subtract two from w “in-place”, i.e., at the end of the computation the tape should contain the result, w − 2 and the tape head should be at the start of that string. Upon a successful operation, halt on accept. Otherwise,...
Discrete Mathematical Structures
Draw a Turing machine that takes a string representing two unary numbers, x and y, separated by a 0, and determines whether x greaterthanorequalto y. For example, the input for x = 3, y = 4 would be 11101111. Use two halt states: one for yes and one for no. Give the trace of your machine in the previous problem processing the strings 11101111 and 11110111. Draw a TM that computes f(w) = w^R where w elementof...
7. (Exercise 8.5.1) Simulating a Turing machine. Here is a description of a Turing machine. The input alphabet is {a, b}. The state set is: {90, 91, 92, 93, 94, qacc, Cre; } The transition function is given in the table below: 90 9 42 93 94 a (qı, a, R) (qı, a, R) (q2, a, R) (qace, a, R) (qej, a, R) b (q2, b, R) (qı, b, R) (qı, b, R) (qrej, b, R) (qace, b, R) **...
40 points) Please design a Turing machine T to recognize the union of the languages of two Turing machines Mi and M2. That is, T accepts an input string w, if and only if either Mi or M2 or both accept string w. Please describe the high-level idea (or algorithm) of your Turing machine T. You do not need to draw the low-level state transition diagram of your Turing machine. Note that the difficulty is that Mi or M2 may...
Show that the language A = {<M1> | the language
accepted by the Turing Machine M1 is 1*} is
not decidable. Present your proof in the style of the proof of Th.
5.3, which shows below.
PROOF We let R be a TM that decides REGULARTm and construct TM S to decide ATM. Then S works in the following manner. S - "On input (M, w), where M is a TM and w is a string: 1. Construct the following...
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