push down automata

Question

Consider the below mentioned PDA M₁ (Q, ∑, Г, δ, q₀, Z, F) which accepts thelanguage L.

Where:

Q={q₀, q₁, q₂, q₃, q₄}

Σ={a,b}

Г={a,b,Z}

Z=initial pushdown symbol

F=set of final states, empty in this case as the string is accepted by null store.

Choose the correct Grammar for the language L accepted by M₁ from the following options.

1. 

S → aaBb|aab, B → aaBb|aab

 

2. 

None of the above.

 

3.

S →aaBb|∊, B →aaBb|aab

 

4.

S →aaBb|aab|∊, B →aaBb|aab