regular language - Finding the DFA -

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create dfa such l subscript 4 = {0,1}* - {0,01}* , list first 5 strings in lexicographic order.

i'm having trouble deducing l subscript 4 implies, language of strings length 4? also, when subtract 2 languages, choose string "1" subtracted empty string, meaning can choose first {0,1}* of length 1 subtracted {0,01}* of length 0?

the language {0,01}* set of strings before each 1 there should 1 0. example 00010001 in language 10000 or 0001111 not. {0,1}* on other hand, strings alphabet {0,1}. subtracting these results language @ least has 1 one , 1's come before 0. example 1111000 in l_4 000000 or 011111 not.


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