MadeEasy Subject Test: Theory of Computation - Pushdown Automata

Question

The language {w| the length of w is odd and it's middle symbol is 0, Wε(0+1)*}

Why do we need a PDA for above language. I don't think we need a PDA for this language. I wrote the following RE. Tell me whats wrong in it:-

[(0+1)(0+1)(0+1)]+0[(0+1)(0+1)(0+1)]+ + (other small left over strings like 0,101,100,001,000..... which are not covered in first part of expression)

Comments

how you say this is correct RE , []⁺ has no restriction so how you sure about middle elements.

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[(0+1)(0+1)(0+1)]⁺0[(0+1)(0+1)(0+1)]⁺   <- This part also generates 1110111111, i.e. 111-0-111-111

It is not in the language, but is generated by your expression.

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ok got it. We can't be sure about middle element. Thanks :)