Prof Franklin, Spring 2009
ECS 120, Homework #2 (Covers Sipser 1.3,1.4)
Due Thurs 16 April, 2009

1. Give regular expressions generating the following languages over alphabet {0,1}:

(a) {w : w starts with 0 and has at most three 1's}

(b) {w : w starts with 1 and has at least one 1}

(c) {w : w has an even number of 0's}

(d) {w : w has 1010 as a substring}


(2) Use the procedure described in Lemma 1.55 to convert the following
    regular expressions (over alphabet {0,1}) to nondeterministic
    finite automata:

(a) 1010(11)*

(b) (11)* union (01)*


(3) Use the procedure described in Lemma 1.60 to convert the folowing
    finite automaton into a regular expression:
     Q = {1,2,3}, start = 1, F = {3}, Sigma = {a,b}, delta = {(1,a) -> 2, (2,b or epsilon) -> 3, (3, a or epsilon) -> 1}


(4) Use the pumping lemma to show that the following language (over
alphabet {0,1}) is not regular: {w : w has more 0's than 1's}.