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