1. By John E. Hopcroft, Rajeev Motwani and Jeffrey D. Ullman
Theory
of Computation
Turing Machine
Source of Slides: Introduction to Automata Theory, Languages, and Computation
By John E. Hopcroft, Rajeev Motwani and Jeffrey D. Ullman
Prof. Muhammad Saeed

2. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Church-Turing’s Thesis
Any mathematical problem solving that can be described by an algorithm can be modeled by a Turing Machine.
Dept. of Computer Science & IT, FUUAST Theory of Computation

3. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Types of Turing Machine
1) Multiple track
2) Shift over Turing Machine
3) Nondeterministic
4) Two way Turing Machine
5) Multitape Turing Machine
6) Multidimensional Turing Machine
7) Composite Turing Machine
8) Universal Turing Machine
Dept. of Computer Science & IT, FUUAST Theory of Computation

4. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Formal Definition
Dept. of Computer Science & IT, FUUAST Theory of Computation

5. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Dept. of Computer Science & IT, FUUAST Theory of Computation

6. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Steps
Start in state q0
Read symbol under head
Write new symbol
Shift left/right
Enter new state qj
Dept. of Computer Science & IT, FUUAST Theory of Computation

7. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Notational Conventions For Turing Machines
Dept. of Computer Science & IT, FUUAST Theory of Computation

8. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
Dept. of Computer Science & IT, FUUAST Theory of Computation

9. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Moves for input 0011:
Moves for input 0010:
Dept. of Computer Science & IT, FUUAST Theory of Computation

10. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Transition Diagram for 0011 input
Dept. of Computer Science & IT, FUUAST Theory of Computation

11. Dept. of Computer Science & IT, FUUAST Theory of Computation
Pushdown Automata
A Turing Machine M computes a function ( proper subtraction) for 0m10n on the tape.
means if m ≥ n then m - n else if m < n then 0
Dept. of Computer Science & IT, FUUAST Theory of Computation

12. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
Dept. of Computer Science & IT, FUUAST Theory of Computation

13. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
Dept. of Computer Science & IT, FUUAST Theory of Computation

14. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Transition Table for the function
Dept. of Computer Science & IT, FUUAST Theory of Computation

15. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Transition Diagram for
Dept. of Computer Science & IT, FUUAST Theory of Computation

16. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Transition Table for the function
Transition Diagram for
Dept. of Computer Science & IT, FUUAST Theory of Computation

17. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

18. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

19. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

20. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X 0 Y 1 B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

21. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X 0 Y 1 B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

22. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X 0 Y 1 B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

23. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X 0 Y 1 B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

24. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y 1 B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

25. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y 1 B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

26. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y Y B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

27. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y Y B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

28. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y Y B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

29. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y Y B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

30. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y Y B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

31. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y Y B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

32. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
A Turing Machine M that accepts the language { 0n1n | n ≥0 }
X X Y Y B B q4
Dept. of Computer Science & IT, FUUAST Theory of Computation

33. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
End of Simulation
Dept. of Computer Science & IT, FUUAST Theory of Computation

34. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

35. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

36. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

37. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

38. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

39. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

40. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

41. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

42. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

43. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

44. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

45. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

46. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

47. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

48. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

49. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

50. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

51. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

52. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

53. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

54. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

55. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

56. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

57. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

58. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

59. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

60. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

61. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

62. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

63. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

64. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

65. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

66. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

67. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

68. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

69. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

70. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

71. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

72. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q3
Dept. of Computer Science & IT, FUUAST Theory of Computation

73. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B q0
Dept. of Computer Science & IT, FUUAST Theory of Computation

74. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

75. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B q1
Dept. of Computer Science & IT, FUUAST Theory of Computation

76. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

77. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

78. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

79. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B q2
Dept. of Computer Science & IT, FUUAST Theory of Computation

80. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B q4
Dept. of Computer Science & IT, FUUAST Theory of Computation

81. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B B q4
Dept. of Computer Science & IT, FUUAST Theory of Computation

82. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B B B B B q4
Dept. of Computer Science & IT, FUUAST Theory of Computation

83. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B 0 1 B B B B B q4
Dept. of Computer Science & IT, FUUAST Theory of Computation

84. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B 0 B B B B B B q4
Dept. of Computer Science & IT, FUUAST Theory of Computation

85. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B B 0 B B B B B B q4
Dept. of Computer Science & IT, FUUAST Theory of Computation

86. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Evaluating function
B B B 0 0 B B B B B B q6
Final State
Dept. of Computer Science & IT, FUUAST Theory of Computation

87. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
End of Simulation
Dept. of Computer Science & IT, FUUAST Theory of Computation

88. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Multiplication
0m10n1
Dept. of Computer Science & IT, FUUAST Theory of Computation

89. Dept. of Computer Science & IT, FUUAST Theory of Computation
Turing Machine
Multiplication
0m10n1
Dept. of Computer Science & IT, FUUAST Theory of Computation

90. Dept. of Computer Science & IT, FUUAST Theory of Computation
END
Dept. of Computer Science & IT, FUUAST Theory of Computation