$1.$ Make a deterministic finite automaton that recognizes all words starting with $001$

$2.$ Construct the deterministic finite automaton that recognizes the language complement of the automaton of problem $1,$ that is$,$ it must recognize all words that DO NOT begin with $001$

$3.$ Minimize the automaton in problem $2.$

$4.$ Calculate the language of the automaton in problem $3.$

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