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Non-Deterministic Finite Automata. Nondeterministic Finite Automaton (NFA). Alphabet =. Alphabet =. Two choices. Alphabet =. Two choices. No transition. No transition. First Choice. First Choice. First Choice. First Choice. All input is consumed. “accept”. Second Choice.

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slide3

Alphabet =

Two choices

slide4

Alphabet =

Two choices

No transition

No transition

slide8

First Choice

All input is consumed

“accept”

slide11

Second Choice

No transition:

the automaton hangs

slide12

Second Choice

Input cannot be consumed

“reject”

slide13

An NFA accepts a string:

when there is a computation of the NFA

that accepts the string

There is a computation:

all the input is consumed and the automaton

is in an accepting state

example
Example

is accepted by the NFA:

“accept”

“reject”

because this

computation

accepts

slide17

First Choice

“reject”

slide20

Second Choice

“reject”

slide21

An NFA rejects a string:

when there is no computation of the NFA

that accepts the string.

For each computation:

  • All the input is consumed and the
  • automaton is in a non final state

OR

  • The input cannot be consumed
example1
Example

is rejected by the NFA:

“reject”

“reject”

All possible computations lead to rejection

slide25

First Choice

No transition:

the automaton hangs

slide26

First Choice

Input cannot be consumed

“reject”

slide29

Second Choice

No transition:

the automaton hangs

slide30

Second Choice

Input cannot be consumed

“reject”

slide31

is rejected by the NFA:

“reject”

“reject”

All possible computations lead to rejection

slide38

all input is consumed

“accept”

String is accepted

slide42

No transition:

the automaton hangs

slide43

Input cannot be consumed

“reject”

String is rejected

slide60

Language accepted

(redundant

state)

slide61

Remarks:

  • The symbol never appears on the
  • input tape
  • Simple automata:
slide62

NFAs are interesting because we can

  • express languages easier than FAs

NFA

FA

formal definition of nfas
Formal Definition of NFAs

Set of states, i.e.

Input aplhabet, i.e.

Transition function

Initial state

Accepting states

formally
Formally

: there is a walk from to

with label

formally1
Formally
  • The language accepted by NFA is:
  • where
  • and there is some

(accepting state)