Use the pumping lemma for regular sets to show that { ww

^{R }| w ∈ (a+b)* } is not a regular set.Design a PDA to accept the language { w ∈ (a+b)* | w contains twice as many a's as b's }

Design a PDA to accept the language { a

^{i}b^{j}c^{k}| i = j or j = k }Let L = { a

^{n}b^{n}a^{n}b^{n }| n≥1 }. Show that L can be expressed as the intersection of two context-free languages.Write a cfg for the set of all strings of balanced parentheses. The parentheses must be properly nested. Some sample strings in the language are (()()), ((()(()()))), ()()()(), etc.

Exercise 7.1.3 [Chomsky Normal Form]