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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 Prof. Busch - LSU

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

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

  4. First Choice Prof. Busch - LSU

  5. First Choice Prof. Busch - LSU

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

  7. Second Choice Prof. Busch - LSU

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

  9. An NFA accepts a string: if there is a computation of the NFA that accepts the string i.e., all the input string is processed and the automaton is in an accepting state Prof. Busch - LSU

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

  11. Rejection example Prof. Busch - LSU

  12. First Choice “reject” Prof. Busch - LSU

  13. Second Choice Prof. Busch - LSU

  14. Second Choice “reject” Prof. Busch - LSU

  15. Another Rejection example Prof. Busch - LSU

  16. First Choice Prof. Busch - LSU

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

  18. Second Choice Prof. Busch - LSU

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

  20. An NFA rejects a string: if 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 accepting state OR • The input cannot be consumed Prof. Busch - LSU

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

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

  23. Language accepted: Prof. Busch - LSU

  24. Lambda Transitions Prof. Busch - LSU

  25. Prof. Busch - LSU

  26. Prof. Busch - LSU

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

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

  29. Rejection Example Prof. Busch - LSU

  30. Prof. Busch - LSU

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

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

  33. Language accepted: Prof. Busch - LSU

  34. Another NFA Example Prof. Busch - LSU

  35. Prof. Busch - LSU

  36. Prof. Busch - LSU

  37. “accept” Prof. Busch - LSU

  38. Another String Prof. Busch - LSU

  39. Prof. Busch - LSU

  40. Prof. Busch - LSU

  41. Prof. Busch - LSU

  42. Prof. Busch - LSU

  43. Prof. Busch - LSU

  44. “accept” Prof. Busch - LSU

  45. Language accepted Prof. Busch - LSU

  46. Another NFA Example Prof. Busch - LSU

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

  48. Remarks: • The symbol never appears on the • input tape • Simple automata: Prof. Busch - LSU

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

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

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