Q5. Consider each of the following languages. L = {0'ʻl' | i, j > 2} L2 = {0ʻl' | i, j > 0 & i > 2j} Lz = {Oʻl°2*[i, j,k > 0 & i > 2j & i = k} a) Is it regular? If yes, prove by giving a regular expression or FA state diagram. If no, prove your answer by using the pumping lemma for regular languages. b) Is it context-free? If yes, give a context-free grammar. If no, prove your answer by using the pumping lemma for context-free languages.

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Q5. Consider each of the following languages.
L = {0ʻl'| i, j > 2}
L2 = {0ʻ1' | i, j > 0 & i > 2j}
L3 = {0ʻl'2*| i, j, k 2 0 & i > 2j & i = k}
a) Is it regular? If yes, prove by giving a regular expression or FA
state diagram. If no, prove your answer by using the pumping
lemma for regular languages.
b) Is it context-free? If yes, give a context-free grammar. If no, prove
your answer by using the pumping lemma for context-free
languages.
Transcribed Image Text:Q5. Consider each of the following languages. L = {0ʻl'| i, j > 2} L2 = {0ʻ1' | i, j > 0 & i > 2j} L3 = {0ʻl'2*| i, j, k 2 0 & i > 2j & i = k} a) Is it regular? If yes, prove by giving a regular expression or FA state diagram. If no, prove your answer by using the pumping lemma for regular languages. b) Is it context-free? If yes, give a context-free grammar. If no, prove your answer by using the pumping lemma for context-free languages.
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