非线性，非确定性和非确定性CFL的例子？

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)?

1. Linear Language : For which Linear grammar is possible( ⊆ CFG) eg
   L ₁ = {a ⁿ b ⁿ | n ≥ 0 }

2. Deterministic Context Free Language(D-CFG) : For which Deterministic Push-Down-Automata(D-PDA) is possible eg
   L ₂ = {a ⁿ b ⁿ c ^m | n ≥ 0, m ≥ 0 }
   L ₂ is unambiguous.

A CF grammar that is not linear is nonlinear .
L _nl = {w: n _a (w) = n _b (w)} is also a Non-Linear CFG .

-- 3. Non-Deterministic Context Free Language(N-CFG) : For which only Non-Deterministic Push-Down-Automata(N-PDA) is possible eg
L ₃ = {ww ^R | w ∈ {a, b} ^* }
L ₃ is also Linear CFG.

--4. Ambiguous CFL : CFL for which only ambiguous CFG is possible
L ₄ = {a ⁿ b ⁿ c ^m | n ≥ 0, m ≥ 0 } U {a ⁿ b ^m c ^m | n ≥ 0, m ≥ 0 }
L ₄ is both non-linear and Ambiguous CFG And Every Ambigous CFL \\subseteq N-CFL.

My Question is:
Whether all non-linear, Non-Deterministic CFL are Ambiguous? If not then I need a example that is non-linear, non-deterministic CFL and also unambiguous?

Given Venn-diagram below:

Also asked here

Answer 1

"IN CONTEXT OF CHOMSHY CLASSIFICATION OF FORMAL LANGUAGE"

(1) L ₃ = {ww ^R | w ∈ {a, b} ^* }

• Language L ₃ 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 L ₃ is unambiguous, nonlinear (due to L _p ), and non-deterministic (due to L ₃ ) (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