Made easy postal course example problem

Question

What will be the DFA for wxw^r where w belongs to (a,b)^+ and x belongs to (a,b)^+

Comments

$a(a+b)^{+}a +b(a+b)^{+}b$

correct me if i am wrong .

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yes, it is correct!

Answer 1

let string be $ baabab$

$WxW^{r}$ can be considered as  ba ab ab  $i.e. here$ $W$ ∈ $ba$ & $x$ ∈ $ab$    OR

                                                        b aaba b $i.e. here$ $W’$ ∈ $b$ & $x’$ ∈ $aaba$

$i.e.$ $start$ $and$ $ends$ $with$ “$a$” $or$ “$b$”

therefore, $L$ = { $a(a+b)^{+}a$ $\cup$  $b(a+b)^{+}b$ }

CROSSCHECK: try “bababa”, it should not be satisfy  and “bababb” should satisfy

Comments

Do i have to derive the dfa by using examples fitting the ques description?

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sometimes you have to!