1. Examples for Finite Automata
Fall 2009
Examples for Finite Automata
CSC3130 Tutorial One
Xiao Linfu
Department of Computer Science & Engineering

2. Outline DFA example NFA example NFA to DFA conversion
Regular Expressions

3. DFA
For every string x, there is a unique path from initial state and associated with x.
x is accepted if and only if this path ends at a accept state. x

4. NFA
For any string x, there may exist none or more than one path from initial state and associated with x.
x is accepted if there is some path that ends at a accept state.

5. Strings With Common Prefix
Construct a DFA that accepts a language L over  = {0, 1} such that L is the set of all strings starting with “101”.
0,1 q1 1 q2 q3 1 q0
start q4
0,1 1
absorbing state
dead state

6. Strings With Common Suffix
Construct a DFA that accepts a language L over  = {0, 1} such that L is the set of all strings ending with “101”. 1 q0
start q1 1
q10
q101 1 1

7. NFA for Common Suffix
We can have a simpler representation for common suffix language using NFA:
Use subset construction to convert it to a DFA. q0
1,0 q1 1 q2 q3 1
start 1 q0
start
q0q1 1
q0q2
q0q1q3 1 1
compare with
previous DFA

8. NFA Example
Construct NFAs for the following languages over the alphabet {a, b, …, z}:
All strings that contain eat or sea or easy
start q2 a q3 t q1 e q4
all q0 q6 q5 s y

9. NFA Example
Construct NFA for the language over the alphabet {a, b, …, z} such that every string doesn’t contain “fool”.
‘f’
dead state
not ‘f’
‘f’
‘f’ q1
‘f’
‘o’ q2 q3
‘l’
start q0 q2
‘o’
not ‘f’,‘o’
not ‘f’,‘l’
not ‘f’,‘o’

10. Regular Expressions - Alphabet X = {a, b, c, d} (a + b)*
all strings containing only a and b
c(a + b + c)*c2
all strings containing only a, b, and c that begin with c and end with cc
3) all strings containing only one b
(a+c+d)*b(a+c+d)*

11. Regular Expressions - Alphabet X = {0, 1} (0 + 1)*
the set of all binary strings
031*04
all strings consisting of three 0’s, followed by any number of 1’s, followed by four 0’s
0*1001*
all strings starting with any number of 0’s, followed by 100, followed by and number of 1’s

12. Thank you!