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5 votes
5 votes
$L = \{ww_rx, \text{ where } w,x \in \{a,b\}^*\}$ is definitely regular $w$ can always be considered to be empty string $(\epsilon).$ So, this just becomes $(a+b)^*$ language.

What about the following one?
Whether $L=\{ww_rx, \text{ where } w,x \in \{a,b\}^+\}$ regular?
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3 votes

It is not regular since you will have to first accept wwr which is a CFL , and then you can have any no of a's and b's ,So you can construct a NPDA for this by accepting wwr by final state and then whenever u see either a or b ,and top of stack is Z0 which is the stack symbol then don't make any transitions to any other state , remain in the same final state and let the stack symbol remain same as Z0 only .

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Durgesh Singh asked Jul 25, 2017
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