Let Σ be a non-empty alphabet and LCE* be a context-free language. Which of the following languages is/are necessarily context-free? Note: For some string w€ Σ*, wR is the string reversal. 1. reverse_1(L) = {xy : ]x, y ≤ Σ*, x € L and yR € L} 2. reverse 2(L) = {x : 3x € Σ*, x € L and x = L} If a language is necessarily context-free, prove your claim. Any construction you make does not require a proof of correctness. If a language is not necessarily context-free, give a counterexample language L which is context- free but for which reverse_i(L) (i = 1, 2) is not context-free. To do so, you must show that your language L is context-free by giving either a PDA which accepts it or a CFG which generates it. You do not need to prove the correctness of your construction but you should explain how it works. In addition, you must give a Pumping lemma proof which shows that reverse; (L) is not

Let Σ be a non-empty alphabet and LCE* be a context-free language. Which of the following languages is/are necessarily context-free? Note: For some string w€ Σ, wR is the string reversal. 1. reverse_1(L) = {xy : ]x, y ≤ Σ, x € L and yR € L} 2. reverse 2(L) = {x : 3x € Σ*, x € L and x = L} If a language is necessarily context-free, prove your claim. Any construction you make does not require a proof of correctness. If a language is not necessarily context-free, give a counterexample language L which is context- free but for which reverse_i(L) (i = 1, 2) is not context-free. To do so, you must show that your language L is context-free by giving either a PDA which accepts it or a CFG which generates it. You do not need to prove the correctness of your construction but you should explain how it works. In addition, you must give a Pumping lemma proof which shows that reverse; (L) is not

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

Problem 1PE

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Bare bones programming language

Bare bones programming language is a low-level programming language that gives a detailed stepwise description of a program. It has a tight program design and in-depth understanding of the toolchain. It is based on the target environment and is used for safe coding practices. C programming language is a type of bare bones programming language.

Question

Let Σ be a non-empty alphabet and LCE* be a context-free language.
Which of the following languages is/are necessarily context-free? Note: For some string w = Σ*,
w is the string reversal.
€
1. reverse_1(L) = {xy : ³x, y ≤ Σ*, x € L and yR € L}
R
2. reverse_2(L) = {x : 3x € Σ*, x € L and x² EL
If a language is necessarily context-free, prove your claim. Any construction you make does not
require a proof of correctness.
If a language is not necessarily context-free, give a counterexample language L which is context-
free but for which reverse_i(L) (i 1, 2) is not context-free. To do so, you must show that
your language L is context-free by giving either a PDA which accepts it or a CFG which generates
it. You do not need to prove the correctness of your construction but you should explain how it
works. In addition, you must give a Pumping lemma proof which shows that reverse; (L) is not
context-free.
=

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Step 1: Analysis of reverse_1(L) and reverse_2(L)

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Step 2: Determining if they are Necessarily Context-Free:

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Step 3: Analyzing if They're Necessarily Context-Free:

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Step 4: Proof that reverse_1(L) is not context-free

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Step 5: reverse_2(L):

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Step 6: Proof that reverse_2(L) is context-free:

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