2.48 Let Σ = {0,1}. Let Ci be the language of all strings that contain a 1 in their middle third. Let C₂ be the language of all strings that contain two is in their middle third. So C₁ {xyz x,ze and y = "1", where |x| = |z|≥ y} and C2 = {xyz|x, z EΣ* and y Є *12*12*, where |x| = |2|≥ |y|}. = a. Show that C₁ is a CFL. b. Show that C2 is not a CFL.

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Could you assist me with question 2.48 and the parts that come along with it, I'm having difficulty with this particular problem and would greatly appreciate your guidance as I'm unsure of the required steps. If possible, please indicate which section relates to part A and part B in your explanation and work calculations for both parts as well.

Can you please label the parts so I know which part is part A and which one is part B.

Σ
2.48 Let = {0,1}. Let C₁ be the language of all strings that contain a 1 in their
middle third. Let C₂ be the language of all strings that contain two 1s in their
middle third. So C₁ = {xyz| x, ze Σ and y Є "1", where |x| = z≥y}
and C₂ = {xyz|x, z EE" and y EΣ*10*10*, where |x| = |||y|}.
a. Show that C₁ is a CFL.
b. Show that C2 is not a CFL.
Transcribed Image Text:Σ 2.48 Let = {0,1}. Let C₁ be the language of all strings that contain a 1 in their middle third. Let C₂ be the language of all strings that contain two 1s in their middle third. So C₁ = {xyz| x, ze Σ and y Є "1", where |x| = z≥y} and C₂ = {xyz|x, z EE" and y EΣ*10*10*, where |x| = |||y|}. a. Show that C₁ is a CFL. b. Show that C2 is not a CFL.
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