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Finite Automata. Finite Automaton. Input. String. Output. “Accept” or “Reject”. Finite Automaton. Transition Graph. initial state. accepting state. transition. state. Initial Configuration. Input String. Reading the Input. Input finished. accept. Rejection.

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Presentation Transcript
finite automaton
Finite Automaton

Input

String

Output

“Accept”

or

“Reject”

Finite

Automaton

transition graph
Transition Graph

initial

state

accepting

state

transition

state

languages accepted by fas
Languages Accepted by FAs
  • FA
  • Definition:
    • The language contains
    • all input strings accepted by
    • = { strings that bring
    • to an accepting state}
example
Example

accept

example1
Example

accept

accept

accept

example2
Example

trap state

accept

formal definition
Formal Definition
  • Finite Automaton (FA)

: set of states

: input alphabet

: transition function

: initial state

: set of accepting states

language accepted by fas
Language Accepted by FAs
  • For a FA
  • Language accepted by :
observation
Observation
  • Language rejected by :
example3
Example

= { all strings with prefix }

accept

example4
Example

= { all strings without

substring }

regular languages
Regular Languages
  • Definition:
  • A language is regular if there is
  • FA such that
  • Observation:
  • All languages accepted by FAs
  • form the family of regular languages
slide55

Examples of regular languages:

{ all strings with prefix }

{ all strings without substring }

There exist automata that accept these

Languages (see previous slides).

slide56

There exist languages which are not Regular:

Example:

There is no FA that accepts such a language

(we will prove this later in the class)