Identify the language

Question

Wxw / w belogs to (a, b) ^*, and x belongs to (a, b) ^+

Regular?

Csl?

Answer 1

i think   ...this is a regular language....

and 

RE=a(a+b)⁺a + b(a+b)⁺b +(a+b)⁺

Comments

I think regular expression is (a+ b) ^+

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yes sure....final RE =(a+b)^{+  .....}

i write it like this...just for better understanding.....

Answer 2

No this is NOT a regular expression.

this expression is "wxw" meaning it should start with w and end with w. So even if we were to consume symbols of w by 'x' we may have a different symbol at the end.

Consider the example : abbbc b abbbc (divided as w x w)

if x consumes bbbc of either side of w then it leaves a and c at both ends. But we want to have the ends same.

Comments

@Warlock lord

it is regular

take w = epsilon and x = (a+b)⁺ , now,

one string in language is (a+b)⁺ and it will absorb all other strings you can think of.

if w ϵ (a+b)⁺ , then it would not be regular and for that your explanation would be correct.

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oh yes I didn't pay heed to the *

My bad