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Finite Automata

Finite Automata. Finite Automaton. Input. String. Output. Finite Automaton. String. Finite Accepter. Input. String. Output. “Accept” or “Reject”. Finite Automaton. Transition Graph. Abba -Finite Accepter. initial state. final state “accept”. transition. state.

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Finite Automata

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  1. Finite Automata Costas Busch - RPI

  2. Finite Automaton Input String Output Finite Automaton String Costas Busch - RPI

  3. Finite Accepter Input String Output “Accept” or “Reject” Finite Automaton Costas Busch - RPI

  4. Transition Graph Abba -Finite Accepter initial state final state “accept” transition state Costas Busch - RPI

  5. Initial Configuration Input String Costas Busch - RPI

  6. Reading the Input Costas Busch - RPI

  7. Costas Busch - RPI

  8. Costas Busch - RPI

  9. Costas Busch - RPI

  10. Input finished Output: “accept” Costas Busch - RPI

  11. Rejection Costas Busch - RPI

  12. Costas Busch - RPI

  13. Costas Busch - RPI

  14. Costas Busch - RPI

  15. Input finished Output: “reject” Costas Busch - RPI

  16. Another Rejection Costas Busch - RPI

  17. Output: “reject” Costas Busch - RPI

  18. Another Example Costas Busch - RPI

  19. Costas Busch - RPI

  20. Costas Busch - RPI

  21. Costas Busch - RPI

  22. Input finished Output: “accept” Costas Busch - RPI

  23. Rejection Costas Busch - RPI

  24. Costas Busch - RPI

  25. Costas Busch - RPI

  26. Costas Busch - RPI

  27. Input finished Output: “reject” Costas Busch - RPI

  28. Formalities • Deterministic Finite Accepter (DFA) : set of states : input alphabet : transition function : initial state : set of final states Costas Busch - RPI

  29. Input Alphabet Costas Busch - RPI

  30. Set of States Costas Busch - RPI

  31. Initial State Costas Busch - RPI

  32. Set of Final States Costas Busch - RPI

  33. Transition Function Costas Busch - RPI

  34. Costas Busch - RPI

  35. Costas Busch - RPI

  36. Costas Busch - RPI

  37. Transition Function Costas Busch - RPI

  38. Extended Transition Function Costas Busch - RPI

  39. Costas Busch - RPI

  40. Costas Busch - RPI

  41. Costas Busch - RPI

  42. Observation: There is a walk from to with label Costas Busch - RPI

  43. Example: There is a walk from to with label Costas Busch - RPI

  44. Recursive Definition Costas Busch - RPI

  45. Costas Busch - RPI

  46. Languages Accepted by DFAs • Take DFA • Definition: • The language contains • all input strings accepted by • = { strings that drive to a final state} Costas Busch - RPI

  47. Example accept Costas Busch - RPI

  48. Another Example accept accept accept Costas Busch - RPI

  49. Formally • For a DFA • Language accepted by : Costas Busch - RPI

  50. Observation • Language rejected by : Costas Busch - RPI

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