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To complete the missing transition labels, we need to ensure that the PDA correctly represents the given context-free grammar (CFG):

Grammar:
- S to xSy | T )
- T to wwT | yT | xx )

*PDA Construction from CFG:*

The PDA accepts strings in the language by simulating the derivations of the CFG.

Initialization and transitions based on state p and r :

From state p to state r, we have λ, λ; S . This means starting with S on the stack.

Transitions based on state t :

λ, T; yT : If the top of the stack is T, we can replace it with yT .

λ, S; T : If the top of the stack is S , we can replace it with T.
λ, T; T :

Missing transition
λ S; T : Missing transition
λ, T; T : Missing transition
y, y; λ: If the top of the stack is y , and the input symbol is y , we can pop y from the stack.
λ, #, λ: If the top of the stack is # , we transition to the final state.

Now, considering the production rules of the CFG and ensuring the PDA matches the derivations:

- For S to xSy :
When we see x , we need to push S and y onto the stack.
The missing transition label is ( x, λ; S y ).

- For S to T :
This is already covered.

- For T to wwT :
When we see w , we push w and T onto the stack.
The missing transition label is ( w, λ; wT ).

- For T to yT ):
This is already covered.

- For T to xx ):
When we see x , we push x onto the stack.
The missing transition label is x, λ; x .

Completing the PDA:

- From state r to state ( t ): λ, S; xSy.
- From state ( t ) to state ( t ):
( x, λ ; x )
( w, λ; w )

Thus, the complete transition labels to add to the PDA are:
- ( x, λ; x )
- ( x, λ; S y )
- ( w, λ ; wT )

By ensuring these transitions, the PDA will correctly simulate the derivations of the CFG and accept the language generated by G .