Let L be defined as the following language over {0,1,2}*: L = {w₁2w2 : W₁, W2₂ € {0, 1}*, w₁ is an anagram of w₂}. Prove that L is not context-free.
Let L be defined as the following language over {0,1,2}*: L = {w₁2w2 : W₁, W2₂ € {0, 1}*, w₁ is an anagram of w₂}. Prove that L is not context-free.
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter10: Classes And Data Abstraction
Section: Chapter Questions
Problem 19PE
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![For 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2F423b7b71-3853-4868-b011-5db0a9ba6ab0%2F4dyec5pe_processed.png&w=3840&q=75)
Transcribed Image Text:For 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.
![Let L be defined as the following language over {0, 1, 2}*:
L = {w₁2w2 : W₁, W₂ € {0,1}*, w₁ is an anagram of w₂} .
Prove that L is not context-free.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2F423b7b71-3853-4868-b011-5db0a9ba6ab0%2Fpjhakm7_processed.png&w=3840&q=75)
Transcribed Image Text:Let L be defined as the following language over {0, 1, 2}*:
L = {w₁2w2 : W₁, W₂ € {0,1}*, w₁ is an anagram of w₂} .
Prove that L is not context-free.
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