Formal Languages Finite Automata

1. Formal Languages Finite Automata

2. Chomsky Hierarchy • Type-0 : Unrestricted;recursively enumerated; phrase structured; turing m/c • Type-1: CSL;LBA • Type-2: CFL;PDA • Type-3:RL:FA

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

4. Transition Graph initial state accepting state transition state

5. Initial Configuration Input String

6. Reading the Input

10. Input finished accept

11. Rejection

15. Input finished reject

16. Acceptance or Rejection?

17. Initial State

18. Rejection reject

19. Language?

20. Another Example

24. Input finished accept

25. Rejection Example

29. Input finished reject

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

31. Example: L(M) = ? accept

32. Example accept

33. Example: L(M) = ? accept accept accept

34. Example accept accept accept

35. Example: L(M) = ? trap state accept

36. Example trap state accept

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

38. Input Alphabet

39. Set of States

40. Initial State

41. Set of Accepting States

42. Transition Function

46. Transition Function

47. Extended Transition Function