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Deterministic Finite Automaton (DFA)

Deterministic Finite Automaton (DFA). Input Tape. String. Output. “Accept” or “Reject”. Finite Automaton. Formal Definition. Deterministic Finite Automaton (DFA). : set of states. : input alphabet. : transition function. : initial state. : set of accepting states.

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Deterministic Finite Automaton (DFA)

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  1. Deterministic Finite Automaton (DFA) Input Tape String Output “Accept” or “Reject” Finite Automaton Costas Busch - RPI

  2. Formal Definition • Deterministic Finite Automaton (DFA) : set of states : input alphabet : transition function : initial state : set of accepting states Costas Busch - RPI

  3. Language Accepted: Costas Busch - RPI

  4. Transition Graph initial state accepting state transition state Costas Busch - RPI

  5. For every state, there is a transition for every symbol in the alphabet Costas Busch - RPI

  6. Set of States Example Costas Busch - RPI

  7. Input Alphabet :the input alphabet never contains Example Costas Busch - RPI

  8. Initial State Example Costas Busch - RPI

  9. Set of Accepting States Example Costas Busch - RPI

  10. Transition Function Describes the result of a transition from state with symbol Costas Busch - RPI

  11. Example: Costas Busch - RPI

  12. Costas Busch - RPI

  13. Transition Table for symbols states Costas Busch - RPI

  14. To accept a string: all the input string is scanned and the last state is accepting To reject a string: all the input string is scanned and the last state is non-accepting Costas Busch - RPI

  15. Initial Configuration head Input Tape Input String Initial state Costas Busch - RPI

  16. Scanning the Input Costas Busch - RPI

  17. Costas Busch - RPI

  18. Costas Busch - RPI

  19. Input finished accept Costas Busch - RPI

  20. A Rejection Case Input String Costas Busch - RPI

  21. Costas Busch - RPI

  22. Costas Busch - RPI

  23. Input finished reject Costas Busch - RPI

  24. Another Rejection Case Tape is empty Input Finished reject Costas Busch - RPI

  25. Extended Transition Function Describes the resulting state after scanning string from state Costas Busch - RPI

  26. Example: Costas Busch - RPI

  27. Costas Busch - RPI

  28. Costas Busch - RPI

  29. Another Example Accept state Accept state Accept state Costas Busch - RPI

  30. Empty Tape Input Finished accept Costas Busch - RPI

  31. Another Example trap state Accept state Costas Busch - RPI

  32. Input String Costas Busch - RPI

  33. Costas Busch - RPI

  34. Costas Busch - RPI

  35. Input finished accept Costas Busch - RPI

  36. A rejection case Input String Costas Busch - RPI

  37. Costas Busch - RPI

  38. Costas Busch - RPI

  39. Input finished reject Costas Busch - RPI

  40. Language Accepted: Costas Busch - RPI

  41. Another Example Alphabet: Language Accepted: Costas Busch - RPI

  42. More DFA Examples Empty language All strings Costas Busch - RPI

  43. Language of the empty string Costas Busch - RPI

  44. = { all strings with prefix } Costas Busch - RPI

  45. ={ all binary strings containing substring } Costas Busch - RPI

  46. ={ all binary strings without substring } Costas Busch - RPI

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