Consider the partially complete $2$PDA given below. This $2$PDA, when complete,

should recognise the language $L$ as defined below:

$L=\{(a{)}^{n+1}bb(a{)}^{n}bb(a{)}^n|n0\}($Assume that the alphabet is $=\{a,b\}.)$

a$.$ What is the purpose of the section of the $2$PDA illustrated in box A$?$

Explain in detail how this purpose is achieved.

b$.$ What is the purpose of the section of the $2$PDA illustrated in box $B?$

Explain clearly what is being done here and how it affects or is affected by

the overall design of the $2$PDA.

c$.$ Complete the $2$PDA by showing what should be included in Box $C$ of the

diagram shown above.

Note that the edges shown in the diagram are the only edges that are

needed between what is outside of Box C and what is needed inside Box C$.$