Example of Non-Linear, UnAmbiguous and Non-Deterministic CFL?

Question

In the Chomsky classification of formal languages, I need some examples of Non-Linear, Unambiguous and also Non-Deterministic Context-Free-Language(N-CFL)?

Answer 1

"IN CONTEXT OF CHOMSHY CLASSIFICATION OF FORMAL LANGUAGE"

(1) L₃ = {ww^R | w ∈ {a, b}^* }

• Language L₃ is a Non-Deterministic Context Free Language, its also Unambiguous and Liner language.

(2) L_p is language of parenthesis matching. There are two terminal symbols "(" and ")".
Grammar for L_p is:

S → SS
S → (S)
S → ()   

• This language is nonlinear, deterministic and unambiguous too.

Language L that is union of L_p and L₃ is unambiguous, nonlinear (due to L_p), and non-deterministic (due to L₃) (Assuming language symbols for both languages are different).

This Language is an example of language in Venn-diagram for which I marked ??.

Also the correct diagram is below:

An ambiguous context free language also be a liner context free