Hello. I really need help in this. Its due tonight thank you.

Given the following empty-stack PDA, (8 points; 4 points for the first 8 blanks) a.Xa.aa.b the language L accepted by the empty-stack PDA is the set of strings over the alphabet {a,b} such that each string has the same number of a's and b's. To transform the PDA into a C-F grammar, for each type of the PDA instructions, we need to construct the corresponding grammar productions. In the following, put the corresponding grammar productions in the blanks on the right for the instructions shown on the left. Type 4: The start state and the PDA instruction ,X/pop as shown below gives: Type 1: The PDA instruction ,X/ pop by itself as shown below gives: The PDA instruction a,b/pop by itself as shown below gives: The PDA instruction b, a/pop by itself as shown below gives: The PDA instruction a,X/ push(a) together with the instructions b,a/pop and ,X/ pop as shown below gives: The PDA instruction b, X/ push(b) together with the instructions a,b/pop and ,X/ pop as shown below gives: The PDA instruction a,a/push(a) together with the instruction b, a/pop (used twice) as shown below gives: The PDA instruction b,b/push(b) together with the instruction a,b/pop (used twice) as shown below gives: There are no Type 2 productions because there are no PDA instructions that perform nop stack operation. Collecting all the productions, we get a context-free grammar whose production set is as follows: (0 points) After simplification, we get (2 points for S; 1 point for A; 1 point for B ) and it is easy to see that this is a C-F grammar for L