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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 Prof. Busch - LSU

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

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

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

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

  6. Scanning the Input Prof. Busch - LSU

  7. Prof. Busch - LSU

  8. Prof. Busch - LSU

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

  10. A Rejection Case Input String Prof. Busch - LSU

  11. Prof. Busch - LSU

  12. Prof. Busch - LSU

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

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

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

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

  18. Empty Tape Input Finished accept Prof. Busch - LSU

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

  20. Input String Prof. Busch - LSU

  21. Prof. Busch - LSU

  22. Prof. Busch - LSU

  23. Input finished accept Prof. Busch - LSU

  24. A rejection case Input String Prof. Busch - LSU

  25. Prof. Busch - LSU

  26. Prof. Busch - LSU

  27. Input finished reject Prof. Busch - LSU

  28. Language Accepted: Prof. Busch - LSU

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

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

  31. Set of States Example Prof. Busch - LSU

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

  33. Initial State Example Prof. Busch - LSU

  34. Set of Accepting States Example Prof. Busch - LSU

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

  36. Example: Prof. Busch - LSU

  37. Prof. Busch - LSU

  38. Prof. Busch - LSU

  39. Transition Table for symbols states Prof. Busch - LSU

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

  41. Example: Prof. Busch - LSU

  42. Prof. Busch - LSU

  43. Prof. Busch - LSU

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

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

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

  48. Language rejected by : Prof. Busch - LSU

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

  50. Language of the empty string Prof. Busch - LSU

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