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Pushdown Automata PDAs

Pushdown Automata PDAs. Pushdown Automaton -- PDA. Input String. Stack. States. Initial Stack Symbol. Stack. Stack. stack head. top. bottom. special symbol. The States. Pop symbol. Input symbol. Push symbol. input. stack. top. Replace. input. stack. top. Push. input.

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Pushdown Automata PDAs

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  1. Pushdown AutomataPDAs Costas Busch - RPI

  2. Pushdown Automaton -- PDA Input String Stack States Costas Busch - RPI

  3. Initial Stack Symbol Stack Stack stack head top bottom special symbol Costas Busch - RPI

  4. The States Pop symbol Input symbol Push symbol Costas Busch - RPI

  5. input stack top Replace Costas Busch - RPI

  6. input stack top Push Costas Busch - RPI

  7. input stack top Pop Costas Busch - RPI

  8. input stack top No Change Costas Busch - RPI

  9. A Possible Transition input stack empty Pop top Costas Busch - RPI

  10. A Bad Transition input Empty stack HALT The automaton Halts in state and Rejects the input string Costas Busch - RPI

  11. A Bad Transition input Empty stack HALT The automaton Halts in state and Rejects the input string Costas Busch - RPI

  12. No transition is allowed to be followed When the stack is empty Empty stack Costas Busch - RPI

  13. A Good Transition input stack Pop top Costas Busch - RPI

  14. Non-Determinism These are allowed transitions in a Non-deterministic PDA (NPDA) Costas Busch - RPI

  15. NPDA: Non-Deterministic PDA Example: Costas Busch - RPI

  16. Execution Example: Time 0 Input Stack current state Costas Busch - RPI

  17. Time 1 Input Stack Costas Busch - RPI

  18. Time 2 Input Stack Costas Busch - RPI

  19. Time 3 Input Stack Costas Busch - RPI

  20. Time 4 Input Stack Costas Busch - RPI

  21. Time 5 Input Stack Costas Busch - RPI

  22. Time 6 Input Stack Costas Busch - RPI

  23. Time 7 Input Stack Costas Busch - RPI

  24. Time 8 Input Stack accept Costas Busch - RPI

  25. A string is accepted if there is a computation such that: All the input is consumed AND The last state is a final state At the end of the computation, we do not care about the stack contents Costas Busch - RPI

  26. The input string is accepted by the NPDA: Costas Busch - RPI

  27. In general, is the language accepted by the NPDA: Costas Busch - RPI

  28. Another NPDA example NPDA Costas Busch - RPI

  29. Execution Example: Time 0 Input Stack Costas Busch - RPI

  30. Time 1 Input Stack Costas Busch - RPI

  31. Time 2 Input Stack Costas Busch - RPI

  32. Time 3 Input Guess the middle of string Stack Costas Busch - RPI

  33. Time 4 Input Stack Costas Busch - RPI

  34. Time 5 Input Stack Costas Busch - RPI

  35. Time 6 Input Stack accept Costas Busch - RPI

  36. Rejection Example: Time 0 Input Stack Costas Busch - RPI

  37. Time 1 Input Stack Costas Busch - RPI

  38. Time 2 Input Stack Costas Busch - RPI

  39. Time 3 Input Guess the middle of string Stack Costas Busch - RPI

  40. Time 4 Input Stack Costas Busch - RPI

  41. Time 5 There is no possible transition. Input Input is not consumed Stack Costas Busch - RPI

  42. Another computation on same string: Input Time 0 Stack Costas Busch - RPI

  43. Time 1 Input Stack Costas Busch - RPI

  44. Time 2 Input Stack Costas Busch - RPI

  45. Time 3 Input Stack Costas Busch - RPI

  46. Time 4 Input Stack Costas Busch - RPI

  47. Time 5 Input No final state is reached Stack Costas Busch - RPI

  48. There is no computation that accepts string Costas Busch - RPI

  49. A string is rejected if there is no computation such that: All the input is consumed AND The last state is a final state At the end of the computation, we do not care about the stack contents Costas Busch - RPI

  50. In other words, a string is rejected if in every computation with this string: The input cannot be consumed OR The input is consumed and the last state is not a final state OR The stack head moves below the bottom of the stack Costas Busch - RPI

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