CS 390 Test II

November 9, 2005

20 points each



1. Construct an $NFA-\Lambda$ that accepts the language corresponding to
$((ab+a)^{*} + bb)^{*}$ from the $NFA$'s that recognize a and b. DO NOT SIMPLIFY.










2. For the following $NFA-\Lambda$, answer the questions below:





(a) Find $\Lambda (\{0, 1, 2\})$

{0, 1, 2, 3, 5, 6}


(b) Find $\delta (0, b)$
Empty set



(c) Find $\delta^{*} (0, b)$

{4, 6, 7}


(d) Find $\delta^{*} (0, ab)$

{3, 4, 6, 7}


3. Indicate which ones of the following statements are true and which ones are false.

(a) $\L _{1} \cap L_{2}$ is regular if $\L _{1}$ and $\L _{2}$ are regular.     True
(b) $\delta^{*}(q, xyz) = \delta^{*}(\delta^{*}(\delta^{*}(q, z), y), x)$     False
(c) $r(p,q,k+1) = r(p,q,k) + r(p,s,k)r(s,s,k)^{*}r(s,q,k)$, where r(p,q,k) is the regular expression for the set of strings that are read by going from state p to state q passing through states numbered not larger than k in a DFA.     False
(d) If a language $L$ is regular, then $L^{+}$ is also regular, where $L^{+} = LL^{*}$.     True
(e) After obtaining the $NFA-\Lambda$ for the union of two $NFA-\Lambda$'s by Kleene's method(i.e. as in Question 1 above), the accepting states of the resultant $NFA-\Lambda$ can be coalesced to form one accepting state without changing the language recognized.     False

4. Click here for Question 4

5. Click here for Question 5