322: CSE Formal Models in Computer Science April 18, 2008 Reading Assignment: Sipser 1.4 Problems:
Assignment #3 Due: Friday, April 25, 2008
1. For the language denoted by each of the following regular expressions, give two strings that are members and two strings that are non-members - a total of four strings for each part. Assume the alphabet = {a, b} in all parts: (a) a(ab) b (b) a b (c) a b a (d) (aba bab) (e) ( a)b (f) (a ba bb) 2. Give regular expressions for the following languages: (a) L3 , which is the language of all valid comments in the C language. Assume for this problem that a valid comment in C starts with /# and ends with #/ with no intervening #/. Assume for simplicity that the alphabet for L3 is = {/, #, a, b}. For example, /#ab#/ and /#a/#b#/ are in L3 while /#ab and /#a#/b#/ are not. (b) L4 = {w|w {0, 1} and w starts with a 1 and has odd length or w starts with a 010 and has length that is a multiple of 3}. 3. Using the construction given by the proof of Lemma 1.55 (1st edition Lemma 1.29) (as shown in Examples 1.57 and 1.58 (1st edition and 1.30 1.31) to draw state diagrams for NFAs that accept the languages given by the following regular expressions. Include all states that would be created by this construction (in other words do not simplify any of the steps in the construction.) (a) ((ab) b) bb . (b) (a b(ab ) b ) 4. Consider the DFA M = ({q0 , q1 , q2 , q3 }, {0, 1}, , q0 , {q1 }) with the following transition function for i = 0, 1, 2, 3; (qi , 0) = q2i mod 4 and (qi , 1) = q2i+1 mod 4 . (a) Let L5 be the language accepted by M . Give a simple description of L5 . (b) Using the NFA to regular expression covered in class, obtain a regular expression that describe...