The last example suggests the conjecture that if a language L is regular, so
are L 2 ,L 3 ,…. We will see later that this is indeed correct.
EXERCISES
1. Which of the strings 0001, 01001, 0000110 are accepted by the dfa in Figure
2.1?
2. For Σ= {a,b}, onstruct dfa's that accept the sets consisting of
(a) all strings with exactly one a,
(b) all strings with at least one a,
(c) all strings with no more than three a's,
(d) all strings with at least one a and exactly two b’s,
(e) all the strings with exactly two a’s and more than two b’s.
3. Show that if we change Figure 2.6, making q 3 a nonfinal state and making q 0 ,
q 1 ,q 2 final states, the resulting dfa accepts
4. Generalize the observation in the previous exercise. Specifically, show that if
M= Q,Σ,δ,q 0 ,F) and
are two dfa's, then
=
5. Give dfa's for the languages
(a)L= {ab 5 wb 2 : w ∈ {a,b} * },