substrings, 0010, contains three zeros.
(e) All strings of length five or more in which the fourth symbol from the
right end is different from the leftmost symbol.
(f) All strings in which the leftmost two symbols and the rightmost two
symbols are identical.
(g) All strings of length four or greater in which the leftmost three
symbols are the same, but different from the rightmost symbol.
* 10. Construct a dfa that accepts strings on {0,1} if and only if the value of the
string, interpreted as a binary representation of an integer, is zero modulo
five. For example, 0101 and 1111, representing the integers 5 and 15,
respectively, are to be accepted.
11. Show that the language L= {vwv: v, w ∈ {a,b} * , |v|= 2} is regular.
12. Show that L= {a n : n ≥4} is regular.
13. Show that the language L= {a n : n ≥ 0,n ≠ 4} is regular.
14. Show that the language L= {a n : n is either a multiple of three or a multiple
of 5} is regular.
15. Show that the language L = {a n : n is a multiple of three, but not a multiple
of 5} is regular.
16. Show that the set of all real numbers in C is a regular language.
17. Show that if L is regular, so is L - {λ}.
18. Show that if L is regular, so is L ∪ {a}, for all a ∈ Σ.
19. Use (2.1) and (2.2) to show that for all w,v ∈ Σ * .
20. Let L be the language accepted by the automaton in Figure 2.2. Find a dfa
that accepts L 2 .
21. Let L be the language accepted by the automaton in Figure 2.2. Find a dfa