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Deterministic
Finite Automata
COMPSCI 102 Lecture 2
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View Full Document Let me show you a
machine so simple
that you can
understand it in less
than two minutes
Steven Rudich:
www.cs.cmu.edu/~rudich
0
0,1
0
0
1
1
1
0111
111
11
1
The machine
accepts
a string if the process
ends in a double circle
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View Full Document Steven Rudich:
www.cs.cmu.edu/~rudich
0
0,1
0
0
1
1
1
The machine
accepts
a string if the process
ends in a double circle
Anatomy of a Deterministic Finite
Automaton
states
states
q
0
q
1
q
2
q
3
start state (q
0
)
accept states (F)
Steven Rudich:
www.cs.cmu.edu/~rudich
Anatomy of a Deterministic Finite
Automaton
0
0,1
0
0
1
1
1
q
0
q
1
q
2
q
3
The
alphabet
of a finite automaton is the set
where the symbols come from:
The
language
of a finite automaton is the set of
strings that it accepts
{0,1}
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View Full Document Steven Rudich:
www.cs.cmu.edu/~rudich
0,1
q
0
L(M) =
All strings of 0s and 1s
∅
The Language of Machine M
Steven Rudich:
www.cs.cmu.edu/~rudich
q
0
q
1
0
0
1
1
L(M) =
{ w  w has an even number of 1s}
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An
alphabet
Σ is a finite set (e.g., Σ = {0,1})
A string over Σ is a finitelength sequence of
elements of Σ
For a string x, x is
the length of x
The unique string of length 0 will be denoted by
ε
and will be called the empty or null string
Notation
A
language over Σ
is a set of strings over Σ
Steven Rudich:
www.cs.cmu.edu/~rudich
Q
is the set of states
Σ
is the alphabet
δ
: Q
×
Σ → Q
is the transition function
q
0
∈
Q
is the start state
F
⊆
Q
is the set of accept states
A finite automaton is a 5tuple
M = (Q, Σ,
δ
, q
0
, F)
L(M) = the language of machine M
= set of all strings machine M accepts
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This document was uploaded on 01/17/2012.
 Fall '09

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