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Non-Deterministic Finite Automata

Non-Deterministic Finite Automata. Nondeterministic Finite Automaton (NFA). Alphabet =. Alphabet =. Two choices. No transition. No transition. First Choice. First Choice. First Choice. All input is consumed. “accept”. Second Choice. Second Choice. Input cannot be consumed.

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Non-Deterministic Finite Automata

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  1. Non-Deterministic Finite Automata Costas Busch - LSU

  2. Nondeterministic Finite Automaton (NFA) Alphabet = Costas Busch - LSU

  3. Alphabet = Two choices No transition No transition Costas Busch - LSU

  4. First Choice Costas Busch - LSU

  5. First Choice Costas Busch - LSU

  6. First Choice All input is consumed “accept” Costas Busch - LSU

  7. Second Choice Costas Busch - LSU

  8. Second Choice Input cannot be consumed Automaton Halts “reject” Costas Busch - LSU

  9. A NFA accepts a string: if there is a computation path of the NFA that accepts the string all the symbols of input string are processed and the last is an accepting state Costas Busch - LSU

  10. is accepted by the NFA: “accept” “reject” because this computation accepts this computation is ignored Costas Busch - LSU

  11. Rejection example Costas Busch - LSU

  12. First Choice “reject” Costas Busch - LSU

  13. Second Choice Costas Busch - LSU

  14. Second Choice “reject” Costas Busch - LSU

  15. Another Rejection example Costas Busch - LSU

  16. First Choice Costas Busch - LSU

  17. First Choice Input cannot be consumed “reject” Automaton halts Costas Busch - LSU

  18. Second Choice Costas Busch - LSU

  19. Second Choice Input cannot be consumed Automaton halts “reject” Costas Busch - LSU

  20. A NFA rejects a string: if there is no computation of the NFA that accepts the string. For each possible computation path: • All the input is consumed and the automaton is in a non accepting state OR • The input cannot be consumed Costas Busch - LSU

  21. is rejected by the NFA: “reject” “reject” All possible computations lead to rejection Costas Busch - LSU

  22. is rejected by the NFA: “reject” “reject” All possible computations lead to rejection Costas Busch - LSU

  23. Language accepted: Costas Busch - LSU

  24. Epsilon Transitions Costas Busch - LSU

  25. Costas Busch - LSU

  26. Costas Busch - LSU

  27. input tape head does not move Automaton changes state Costas Busch - LSU

  28. all input is consumed “accept” String is accepted Costas Busch - LSU

  29. Rejection Example Costas Busch - LSU

  30. Costas Busch - LSU

  31. (read head doesn’t move) Costas Busch - LSU

  32. Input cannot be consumed Automaton halts “reject” String is rejected Costas Busch - LSU

  33. Language accepted: Costas Busch - LSU

  34. Another NFA Example Costas Busch - LSU

  35. Costas Busch - LSU

  36. Costas Busch - LSU

  37. “accept” Costas Busch - LSU

  38. Another String Costas Busch - LSU

  39. Costas Busch - LSU

  40. Costas Busch - LSU

  41. Costas Busch - LSU

  42. Costas Busch - LSU

  43. Costas Busch - LSU

  44. “accept” Costas Busch - LSU

  45. Language accepted Costas Busch - LSU

  46. Another NFA Example Costas Busch - LSU

  47. Language accepted (redundant state) Costas Busch - LSU

  48. Simple Automata Costas Busch - LSU

  49. NFAs are interesting because we can express languages easier than DFAs NFA DFA Costas Busch - LSU

  50. Formal Definition of NFAs Set of states, i.e. Input aplhabet, i.e. Transition function Initial state Accepting states Costas Busch - LSU

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