Question: Please provide a new answer, don't copy from other posts; thank you! Call a string x {0,1}prefix-balanced if, for every prefix w of x, |

Please provide a new answer, don't copy from other posts; thank you!

Call a string x {0,1}prefix-balanced if, for every prefix w of x, | # (0,w) # (1,w) | 1.

Design a DFA M such that L(M) = { x {0,1} | x is prefix-balanced and # (0,x) = # (1,x)}.

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