# doc

CS311-Automata and Complexity Theory
Homework 03
Due Date: Monday, 5th Jan 2004 (at the beginning of class)
1. [20 points] In each of the following, find a simpler regular expression.
a.
b.
c.
d.
0*(01)*1*
(0*+1*)(0*+1*)(0*+1*)
0*(100*)*1*
1*(0+10)*1*
2. [10 points] Apply theorem 3.4 to obtain a regular expression for the language
accepted by the following DFA:
a
a
b
b
Show all working.
3. [10 points] Find the regular expression corresponding to the following FA,
through the state elimination technique. Show all working.
4. [10 points] Construct an NFA, and then a DFA for the language accepting the
language L that corresponds to the following regular expression:
(11 + 110)0*
5. [10 points] Find the language and the corresponding regular expression of the
following FA. Show all working.
Start state: Q0
Final State: Q6
The transition table:
State
Q0
Q1
Q2
Q3
Q4
Q5
Q6
δ(Q,0)
Q1
Q3
Q5
Q3
Q5
Q3
Q5
δ(Q,1)
Q2
Q4
Q6
Q4
Q6
Q4
Q6
6. [10 points] Give the language and corresponding regular expression for the
following FA:
7. [30 points] Draw an FA recognizing the language corresponding to the following
regular expressions:
a. (0 + 1)*0
b. (11 + 10)*
c. (1 + 110)*0
d. (111 + 100)*0
e. 1(01 + 10)* + 0(11 +10)*
f. 1(1+10)* +10(0 + 01)*