Give regular expressions generating the languages of Exercise 1.6.
Exercise 1.6
Give state diagrams of DFAs recognizing the following languages. In all parts, the alphabet is {0,1}.
a. {w| w begins with a 1 and ends with a 0}
b. {w| w contains at least three 1s}
c. {w| w contains the substring 0101 (i.e., w = x0101y for some x and y)}
d. {w| w has length at least 3 and its third symbol is a 0}
e. {w| w starts with 0 and has odd length, or starts with 1 and has even length}
f. {w| w doesn’t contain the substring 110}
g. {w| the length of w is at most 5}
h. {w| w is any string except 11 and 111}
i. {w| every odd position of w is a 1}
j. {w| w contains at least two 0s and at most one 1}
k. {“, 0}
l. {w| w contains an even number of 0s, or contains exactly two 1s}
m. The empty set
n. All strings except the empty string
