Michael Sipser Edition 3 Exercise 2 Question 29 (Page No. 157)

Question

Show that the language $A=\{a^{i}b^{j}c^{k}\mid i=j$  $\text{or}$ $ j=k$  $\text{where}$ $ i,j,k\geq 0\}$ is inherently ambiguous$.$

Comments

the language has non-deterministic PDA. it is union of two languages

$a^nb^nc^m \cup a^mb^nc^n$

the ambiguity cannot be removed. so it is inherently ambiguous