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Deterministic Finite Automata And Regular Languages

Deterministic Finite Automata And Regular Languages. Deterministic Finite Automaton (DFA). Input Tape. String. Output. “Accept” or “Reject”. Finite Automaton. Transition Graph. initial state. accepting state. transition. state. Alphabet.

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Deterministic Finite Automata And Regular Languages

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  1. Deterministic Finite Automata And Regular Languages Costas Busch - LSU

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

  3. Transition Graph initial state accepting state transition state Costas Busch - LSU

  4. Alphabet For every state, there is a transition for every symbol in the alphabet Costas Busch - LSU

  5. Initial Configuration head Input Tape Input String Initial state Costas Busch - LSU

  6. Scanning the Input Costas Busch - LSU

  7. Costas Busch - LSU

  8. Costas Busch - LSU

  9. Input finished accept Last state determines the outcome Costas Busch - LSU

  10. A Rejection Case Input String Costas Busch - LSU

  11. Costas Busch - LSU

  12. Costas Busch - LSU

  13. Input finished reject Last state determines the outcome Costas Busch - LSU

  14. Another Rejection Case Tape is empty Input Finished (no symbol read) reject Costas Busch - LSU

  15. This automaton accepts only one string Language Accepted: Costas Busch - LSU

  16. 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 - LSU

  17. Another Example Accept state Accept state Accept state Costas Busch - LSU

  18. Empty Tape Input Finished accept Costas Busch - LSU

  19. Another Example trap state Accept state Costas Busch - LSU

  20. Input String Costas Busch - LSU

  21. Costas Busch - LSU

  22. Costas Busch - LSU

  23. Input finished accept Costas Busch - LSU

  24. A rejection case Input String Costas Busch - LSU

  25. Costas Busch - LSU

  26. Costas Busch - LSU

  27. Input finished reject Costas Busch - LSU

  28. Language Accepted: Costas Busch - LSU

  29. Another Example Alphabet: Language Accepted: Costas Busch - LSU

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

  31. Set of States Example Costas Busch - LSU

  32. Input Alphabet :the input alphabet never contains Example Costas Busch - LSU

  33. Initial State Example Costas Busch - LSU

  34. Set of Accepting States Example Costas Busch - LSU

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

  36. Example: Costas Busch - LSU

  37. Costas Busch - LSU

  38. Costas Busch - LSU

  39. Transition Table for symbols states Costas Busch - LSU

  40. Extended Transition Function Describes the resulting state after scanning string from state Costas Busch - LSU

  41. Example: Costas Busch - LSU

  42. Costas Busch - LSU

  43. Costas Busch - LSU

  44. Special case: for any state Costas Busch - LSU

  45. In general: implies that there is a walk of transitions states may be repeated Costas Busch - LSU

  46. Language Accepted by DFA Language accepted by DFA : it is denoted as and contains all the strings accepted by We also say that recognizes Costas Busch - LSU

  47. For a DFA Language accepted by : Costas Busch - LSU

  48. Language rejected by : Costas Busch - LSU

  49. More DFA Examples Empty language All strings Costas Busch - LSU

  50. Language of the empty string Costas Busch - LSU

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