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.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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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.
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.
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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