Chapter 2
Finite Automata

Learning Outcomes
At the end of the module, the student must be
able to:
•
describe language accepted by a given
automata.
•
construct finite automata for a given regular
language.

Topics
•
Deterministic Finite Accepters (DFA)
•
Nondeterministic Finite Accepters (NFA)

DFA (2.1)
•
Deterministic Finite Acceptors
•
Example DFA
•
Formal Definition of a DFA
•
Languages and Regular Languages
•
Several examples

DFA (2.1)
Deterministic Finite Acceptors
•
DFAs are:
–
Deterministic--there is no element of choice
–
Finite--only a finite number of states and arcs
–
Acceptors--produce only a yes/no answer
•
A DFA is drawn as a graph, with each state represented by a circle.
start state
•
One designated state is the start state.
final state
•
Some states (possibly including the start state) can be designated as final states.
transition
•
Arcs between states represent state transitions -- each such arc is labeled with the
symbol that triggers the transition.

DFA (2.1)
Formal Definition of a DFA
•
A deterministic finite acceptor or dfa is a quintuple:
M = (Q,
,
, q
0
, F)
where
Q is a finite set of
internal states
,
is a finite set of symbols, the
input alphabet
,
: Q
Q is a
transition function
,
q
0
Q is the
initial state
,
F
Q is a set of
final states
.
•
Note: The fact that
is a function implies that every vertex has
an outgoing arc for each member of
.

The graph in Fig. represent
the dfa
M = ({q
0
,q
1
,q
2
}, {0,1},
, q
0
, {q
1
})
where
is given by
(q
0
,0)= q
0
(q
0
,1)= q
1
(q
1
,0)= q
0
(q
1
,1)= q
2
(q
2
,0)= q
2
(q
2
,1)= q
1
DFA (2.1)
Example DFA

Question
Based on the given DFA,
trace the following input string:
1 0 1, 0111, 100, 1100
Analysis
•
Start with the

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- Fall '16
- Jennifer Smith
- Formal language, Regular expression, Regular language, Nondeterministic finite state machine, Automata theory