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Understanding Pushdown Automata: Basics, Examples, and Computations

Learn about pushdown automata theory, execution examples, acceptance, rejection, and non-determinism. Explore detailed explanations and computation walkthroughs.

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Understanding Pushdown Automata: Basics, Examples, and Computations

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  1. Pushdown AutomataPDAs Costas Busch - LSU

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

  3. Initial Stack Symbol Stack Stack stack head top bottom special symbol Appears at time 0 Costas Busch - LSU

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

  5. input stack top Replace Costas Busch - LSU

  6. input stack top Push Costas Busch - LSU

  7. input stack top Pop Costas Busch - LSU

  8. input stack top No Change Costas Busch - LSU

  9. Non-Determinism PDAs are non-deterministic Allowed non-deterministic transitions Costas Busch - LSU

  10. Example PDA PDA : Costas Busch - LSU

  11. Basic Idea: • Push the a’s on the stack 2. Match the b’s on input with a’s on stack 3. Match found Costas Busch - LSU

  12. Execution Example: Time 0 Input Stack current state Costas Busch - LSU

  13. Time 1 Input Stack Costas Busch - LSU

  14. Time 2 Input Stack Costas Busch - LSU

  15. Time 3 Input Stack Costas Busch - LSU

  16. Time 4 Input Stack Costas Busch - LSU

  17. Time 5 Input Stack Costas Busch - LSU

  18. Time 6 Input Stack Costas Busch - LSU

  19. Time 7 Input Stack Costas Busch - LSU

  20. Time 8 Input Stack accept Costas Busch - LSU

  21. A string is accepted if there is a computation such that: All the input is consumed AND The last state is an accepting state we do not care about the stack contents at the end of the accepting computation Costas Busch - LSU

  22. Rejection Example: Time 0 Input Stack current state Costas Busch - LSU

  23. Rejection Example: Time 1 Input Stack current state Costas Busch - LSU

  24. Rejection Example: Time 2 Input Stack current state Costas Busch - LSU

  25. Rejection Example: Time 3 Input Stack current state Costas Busch - LSU

  26. Rejection Example: Time 4 Input Stack current state Costas Busch - LSU

  27. Rejection Example: Time 4 Input Stack reject current state Costas Busch - LSU

  28. There is no accepting computation for The string is rejected by the PDA Costas Busch - LSU

  29. Another PDA example PDA : Costas Busch - LSU

  30. Basic Idea: • Push v on stack 3. Match on input with v on stack 2. Guess middle of input 4. Match found Costas Busch - LSU

  31. Execution Example: Time 0 Input Stack Costas Busch - LSU

  32. Time 1 Input Stack Costas Busch - LSU

  33. Time 2 Input Stack Costas Busch - LSU

  34. Time 3 Input Guess the middle of string Stack Costas Busch - LSU

  35. Time 4 Input Stack Costas Busch - LSU

  36. Time 5 Input Stack Costas Busch - LSU

  37. Time 6 Input Stack accept Costas Busch - LSU

  38. Rejection Example: Time 0 Input Stack Costas Busch - LSU

  39. Time 1 Input Stack Costas Busch - LSU

  40. Time 2 Input Stack Costas Busch - LSU

  41. Time 3 Input Guess the middle of string Stack Costas Busch - LSU

  42. Time 4 Input Stack Costas Busch - LSU

  43. Time 5 There is no possible transition. Input Input is not consumed Stack Costas Busch - LSU

  44. Another computation on same string: Input Time 0 Stack Costas Busch - LSU

  45. Time 1 Input Stack Costas Busch - LSU

  46. Time 2 Input Stack Costas Busch - LSU

  47. Time 3 Input Stack Costas Busch - LSU

  48. Time 4 Input Stack Costas Busch - LSU

  49. Time 5 Input No accept state is reached Stack Costas Busch - LSU

  50. There is no computation that accepts string Costas Busch - LSU

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