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Alphabet is {a,b}, the third element from the start must be "b" (e.g: aab..., abb...) and the third-last element must also be "b" (e.g: ...baa, ...bbb). I can do them separately but at the same time I don't know where to start. Help please.

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Hint. If $A$ is the alphabet, a regular expression for your language is $AAbA^*bAA \cup AAbAA \cup AbbA \cup bAb$.

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  • $\begingroup$ @G.Bach I wrote both my answer and in my answer to your comment in a hurry, but now that I have more time, I would like to thank you for pointing out my mistake in this elegant way. $\endgroup$ – J.-E. Pin May 27 '16 at 16:06
  • $\begingroup$ Thank you! That's right, since the automaton is nondeterministic, I can just concatenate the three of them (bxb, xbbx and xxbxx), it works now. $\endgroup$ – Marx Guimarães May 28 '16 at 17:25

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