is correct this Pumping Lemma? and this?

From: FlicK (zeldino_at_hotmail.com)
Date: 02/20/04 

Date: Fri, 20 Feb 2004 17:40:28 GMT

Prove that L = {a^n b^n+2 | n > 0} on alphabet {a, b} is not regular
with Pumping Lemma.

For all n exist a word | not satisfy the P.L. with three rule:

1. |xy| <= n
2. |y| > 0
3. xy^iz belong L for all i >= 0

Factorize

w = xyz = a^n-k a^k b^n+2 with 0 < k <= n

and this expression satisfy rule 1 and 2 but not 3, therefore xz =
a^n-k b^n+2 with k > 0 and xz not belong L... is not regular

is it correct?

The other questions is:

an authome DFA with this peculiarity:

L = {a, b} with odd word-length and end with ba OR word-length is a
multiple of 3.

What is the correct DFA autome? is correct this:

0 epsilon with state 1 and 6
state 1 a
state 2 a
state 3 b
state 2 a
state 3 b (in loop) then read b, a and accept
OR
state 6 a
state 7 b
state 8 a
state 9 return in 6 and continue in loop

thanks!

Thank you very much!