The document describes how a deterministic finite automaton (DFA) works to accept or reject an input string. A DFA has a finite set of states, transitions between states based on input symbols, an initial state, and accepting states. It scans the input string one symbol at a time, moving between states based on transitions, and accepts the string if it ends in an accepting state.

1. Fall 2006 Costas Busch - RPI 1
Deterministic Finite Automaton (DFA)
Input Tape
“Accept”
or
“Reject”
String
Finite
Automaton
Output

2. Fall 2006 Costas Busch - RPI 2
Transition Graph
initial
state
accepting
state
state
transition
0q 1q 2q 3q 4qa b b a
5q
a a bb
ba,
ba,

3. Fall 2006 Costas Busch - RPI 3
0q 1q 2q 3q 4qa b b a
5q
a a bb
ba,
ba,
},{ ba=Σ
For every state, there is a transition
for every symbol in the alphabet
Alphabet

4. Fall 2006 Costas Busch - RPI 4
Initial Configuration
1q 2q 3q 4qa b b a
5q
a a bb
ba,
Input String
a b b a
ba,
0q
Initial state
Input Tape
head

5. Fall 2006 Costas Busch - RPI 5
Scanning the Input
0q 1q 2q 3q 4qa b b a
5q
a a bb
ba,
a b b a
ba,

6. Fall 2006 Costas Busch - RPI 6
0q 1q 2q 3q 4qa b b a
5q
a a bb
ba,
a b b a
ba,

7. Fall 2006 Costas Busch - RPI 7
0q 1q 2q 3q 4qa b b a
5q
a a bb
ba,
a b b a
ba,

8. Fall 2006 Costas Busch - RPI 8
0q 1q 2q 3q 4qa b b a
accept
5q
a a bb
ba,
a b b a
ba,
Input finished