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Understanding Pushdown Automata: Examples and Execution

Learn the basics of pushdown automata (PDAs) through Costas Busch's detailed examples and step-by-step execution scenarios. Explore the concepts of stack manipulation, states, input processing, and acceptance/rejection criteria.

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Understanding Pushdown Automata: Examples and Execution

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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 Appears at time 0 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. Pop from Empty Stack input Pop Automaton halts! stack top If the automaton attempts to pop from empty stack then it halts and rejects input Costas Busch - RPI

  10. Non-Determinism PDAs are non-deterministic Allowed non-deterministic transitions Costas Busch - RPI

  11. Example PDA PDA : Costas Busch - RPI

  12. 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 - RPI

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

  14. Time 1 Input Stack Costas Busch - RPI

  15. Time 2 Input Stack Costas Busch - RPI

  16. Time 3 Input Stack Costas Busch - RPI

  17. Time 4 Input Stack Costas Busch - RPI

  18. Time 5 Input Stack Costas Busch - RPI

  19. Time 6 Input Stack Costas Busch - RPI

  20. Time 7 Input Stack Costas Busch - RPI

  21. Time 8 Input Stack accept Costas Busch - RPI

  22. 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 - RPI

  23. Rejection Example: Time 0 Input Stack current state Costas Busch - RPI

  24. Rejection Example: Time 1 Input Stack current state Costas Busch - RPI

  25. Rejection Example: Time 2 Input Stack current state Costas Busch - RPI

  26. Rejection Example: Time 3 Input Stack current state Costas Busch - RPI

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

  28. Rejection Example: Time 4 Input Stack reject current state Costas Busch - RPI

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

  30. Another PDA example PDA : Costas Busch - RPI

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

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

  33. Time 1 Input Stack Costas Busch - RPI

  34. Time 2 Input Stack Costas Busch - RPI

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

  36. Time 4 Input Stack Costas Busch - RPI

  37. Time 5 Input Stack Costas Busch - RPI

  38. Time 6 Input Stack accept Costas Busch - RPI

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

  40. Time 1 Input Stack Costas Busch - RPI

  41. Time 2 Input Stack Costas Busch - RPI

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

  43. Time 4 Input Stack Costas Busch - RPI

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

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

  46. Time 1 Input Stack Costas Busch - RPI

  47. Time 2 Input Stack Costas Busch - RPI

  48. Time 3 Input Stack Costas Busch - RPI

  49. Time 4 Input Stack Costas Busch - RPI

  50. Time 5 Input No accept state is reached Stack Costas Busch - RPI

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