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Pushdown Automata PDAs

Explore the working principles of Pushdown Automaton (PDA) presented by Costas Busch from RPI. Learn about input, stack, states transition, and computation examples in non-deterministic PDAs.

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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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