L₁ {abck i, j, k EN such that i < j and j > k} L₂ = { aibi+nck : i, j, k, n € N such that i + j < n+k} = For each language decide whether it is 1. Regular. 2. Not regular, but context-free. 3. Not context-free. If you answer "Regular" for a language, you must provide an FA (DFA, NFA, NFA+e) which accepts it or a regular expression which describes it. If you answer "Not regular, but context free", you must show that the language is not regular using any method/fact seen in class and provide either a CFG which generates it or a PDA (DPDA, NPDA) which accepts it. If you answer "Not context-free", you must provide a Pumping lemma proof. You do not need to prove the correctness of any of your constructions but you should explain how they work.

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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Consider the following languages over the alphabet Σ = {a, b, c}.

L₁ = {a¹b³ck : ‡i, j, k = N such that i < j and j > k}
L2 = {aibi+nck : \i, j, k,n ¤ N such that i + j < n+k}
For each language decide whether it is
1. Regular.
2. Not regular, but context-free.
3. Not context-free.
If you answer "Regular" for a language, you must provide an FA (DFA, NFA, NFA+ɛ) which
accepts it or a regular expression which describes it. If you answer "Not regular, but context-
free”, you must show that the language is not regular using any method/fact seen in class and
provide either a CFG which generates it or a PDA (DPDA, NPDA) which accepts it. If you
answer "Not context-free", you must provide a Pumping lemma proof. You do not need to prove
the correctness of any of your constructions but you should explain how they work.
Transcribed Image Text:L₁ = {a¹b³ck : ‡i, j, k = N such that i < j and j > k} L2 = {aibi+nck : \i, j, k,n ¤ N such that i + j < n+k} For each language decide whether it is 1. Regular. 2. Not regular, but context-free. 3. Not context-free. If you answer "Regular" for a language, you must provide an FA (DFA, NFA, NFA+ɛ) which accepts it or a regular expression which describes it. If you answer "Not regular, but context- free”, you must show that the language is not regular using any method/fact seen in class and provide either a CFG which generates it or a PDA (DPDA, NPDA) which accepts it. If you answer "Not context-free", you must provide a Pumping lemma proof. You do not need to prove the correctness of any of your constructions but you should explain how they work.
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