Finding minimal DFA for language

Question

Find minimal DKA for language of all words in alphabet $ \left\{ 0,1 \right\}^* $ in which every double zero $00$ comes before every double one $11$. Also find the regular expression for the language. $$$$ I tried constructing a NFA epsilon, but I am not sure if my logic is correct.

Answer 1

The regular expression $1^*(011^*)^*(00^*1)^*0^*$ was proposed by Ekesh Kumar in this answer. Here is its minimal automaton:

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