Finite Automata

1. Finite Automata

2. Finite Automaton Input String Output “Accept” or “Reject” Finite Automaton

3. Transition Graph initial state accepting state transition state

4. Initial Configuration Input String

5. Reading the Input

9. Input finished accept

10. Rejection

14. Input finished reject

15. Another Rejection

16. reject

17. Another Example

21. Input finished accept

22. Rejection Example

26. Input finished reject

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

28. Example accept

29. Example accept accept accept

30. Example trap state accept

31. Formal Definition • Finite Automaton (FA) : set of states : input alphabet : transition function : initial state : set of accepting states

32. Input Alphabet

33. Set of States

34. Initial State

35. Set of Accepting States

36. Transition Function

40. Transition Function

41. Extended Transition Function

45. Observation: if there is a walk from to with label then

46. Example: There is a walk from to with label

47. Recursive Definition

49. Language Accepted by FAs • For a FA • Language accepted by :

50. Observation • Language rejected by :