Peter Linz Edition 4 Exercise 5.1 Question 14 (Page No. 134)

Question

Let $L_1$ be the language $L_1 =$ {$a^nb^mc^k : n = m$ or $m ≤ k$} and $L_2$ the language $L_2 =$ {$a^nb^mc^k : n + 2m = k$}. Show that $L_1 ∪ L_2$ is a context-free language.

Answer 1

 

S→ AB | CDE | F

A→aAb |  λ

B→ Bc  |  λ
C→ aC  |  λ

D→bDc | λ
E→ Ec   |  λ

F→aFc | G

G→bGcc | λ