(a) (12pts) Give state diagrams of DFAs recognizing the following languages. The alphabet is {0,1}.
o L = {w | w begins with 0 and ends with 1}
o L2 = {w | w has length 4 and its third symbol is a 0}
o L3 = {w | the length of w is at most 3}
o L4 = {w | contains at least three 1s}
(b) (4pts) Write the formal definition of one of the previous DFAs.
(c) (4pts) Construct a DFA that accepts strings over alphabet {a,b,c} whose symbols are in alphabetical order (for example: aabcc, bc, and acc are accepted but not acb or abca).
(d) (8pts) Give state diagrams of DFAs recognizing the following languages. The alphabet is {a,b}.
o L = {ww | any string that does not contain the substring aab}
o L6 = {w | w ∈ A where A = * - {a,aa,b}}
(e) (4pts) Give state diagrams of DFAs recognizing the following L7 = {w | w is not divisible by 5}. The alphabet is {0,1}.