Problem 1: Designing Context-Free Grammar Let Σ₁ = {0, 1,2,3} and E₂ = {a, b}. Consider the following two languages. L₁ = {w Σ₂: the length of w is divisible by three} L₂ = {w € ₁ : w :w=0¹1/2*3m where i = m, j≥ 3k +2 and i, j, k, m >0} (a) Design a context-free grammar whose language is L1. (b) Design a context-free grammar whose language is L₂. .I

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Problem 1: Designing Context-Free Grammar
Let Σ₁ = {0, 1,2,3} and Σ₂ = {a, b}. Consider the following two languages.
L₁ = {w ₂: the length of w is divisible by three}
L₂ = {w€ ₁ : w=0¹1/2k3m where i=m, j ≥ 3k + 2 and i, j, k, m >0}
(a) Design a context-free grammar whose language is L₁.
(b) Design a context-free grammar whose language is L2.
.[
Transcribed Image Text:Problem 1: Designing Context-Free Grammar Let Σ₁ = {0, 1,2,3} and Σ₂ = {a, b}. Consider the following two languages. L₁ = {w ₂: the length of w is divisible by three} L₂ = {w€ ₁ : w=0¹1/2k3m where i=m, j ≥ 3k + 2 and i, j, k, m >0} (a) Design a context-free grammar whose language is L₁. (b) Design a context-free grammar whose language is L2. .[
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