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### Turing machine

• 1.
• 2. ε ε a0 a1 … an ε ε … RD Input Tape Head Finite Control qi
• 3.  Create a Turing Machine that takes as input a string consists of different parentheses ( ), [ ] or { } and ensure if that string is balanced – open parentheses are balanced with closed parentheses – and correct – the smaller one does not include the bigger –.  Examples: {[[(()())]()]} Accepted (balanced and correct) [(())(){()()}] Rejected (balanced but wrong) {[()}}{[(())]} Rejected (correct but unbalanced) {()([])}[(()]] Rejected (unbalanced and wrong)
• 4. Q = { Start , Find1 , Find2 , Find3 , End , Rejected , Accepted } States Description : Start : initial state, that begin to find first symbol ), ] or } then check it with X, Y or Z respectively. Find1 : moving left to find matched symbol (, then check it with X and return to Start state. Find2 : moving left to find matched symbol [, then check it with Y and return to Start state. Find3 : moving left to find matched symbol {, then check it with Z and return to Start state. End : the string is finished, thus moving left to ensure that all symbols are checked. Rejected : there are unchecked (unbalanced) symbols or the string is wrong, therefore string is rejected. Accepted : all symbols are checked (balanced) and the string is correct, therefore string is accepted.
• 5. Γ ={(,),[,],{,},X,Y,Z,ε} (Tape Alphabet) Σ ={(,),[,],{,}} (Input Alphabet) F = { Accepted } (Finite States) Initial State: Start Blank Symbol: ε
• 6. δ(q , γ) ( ) [ ] { } X Y Z ε Start Start Find1 Start Find2 Start Find3 Start Start Start End →),],} (,R X,L [,R Y,L {,R Z,L X,R Y,R Z,R ε,L Rejected Rejected Rejected Rejected Rejected Find1 Start Find1 ( X,R - [,L - {,L - X,L Y,L Z,L ε ,R (wrong) (wrong) (wrong) (wrong) (unbalanced) Rejected Rejected Rejected Rejected Find2 - Start Find2 Find2 [ (,L Y,R - {,L - X,L Y,L Z,L ε ,R (unbalanced) (wrong) (wrong) (unbalanced) Rejected Rejected Rejected Find3 Start Find3 Find3 Find3 { (,L - [,L - Z,R - X,L Y,L Z,L ε,R (unbalanced) (unbalanced) (unbalanced) Accepted End Rejected Rejected Rejected End End End ε,R (,L - [,L - {,L - ε (unbalanced) (unbalanced) (unbalanced) X,L Y,L Z,L (correct) (balanced) Rejected Stop - - - - - - - - - - Accepted Stop - - - - - - - - - -
• 7. X/X,L Find 1 Y/Y,L [/Y,R ε/ε,R Find Accept End ε/ε,L Start (/(,L {/{,L Z/Z,L ε/ε,L Reject 2 ]/Y,L Y/Y,L Find 3 X/Y,D X : Scanned Symbol Y : Written Symbol [/[,L D : Move Direction
• 8. A. The string: {[()]} … ε { [ ( ) ] } ε … Start
• 9. A. The string: {[()]} … ε { [ ( ) ] } ε … Start
• 10. A. The string: {[()]} … ε { [ ( ) ] } ε … Start
• 11. A. The string: {[()]} … ε { [ ( ) ] } ε … Start
• 12. A. The string: {[()]} … ε { [ ( X ] } ε … Find1
• 13. A. The string: {[()]} … ε { [ X X ] } ε … Start
• 14. A. The string: {[()]} … ε { [ X X ] } ε … Start
• 15. A. The string: {[()]} … ε { [ X X Y } ε … Find2
• 16. A. The string: {[()]} … ε { [ X X Y } ε … Find2
• 17. A. The string: {[()]} … ε { [ X X Y } ε … Find2
• 18. A. The string: {[()]} … ε { Y X X Y } ε … Start
• 19. A. The string: {[()]} … ε { Y X X Y } ε … Start
• 20. A. The string: {[()]} … ε { Y X X Y } ε … Start
• 21. A. The string: {[()]} … ε { Y X X Y } ε … Start
• 22. A. The string: {[()]} … ε { Y X X Y Z ε … Find3
• 23. A. The string: {[()]} … ε { Y X X Y Z ε … Find3
• 24. A. The string: {[()]} … ε { Y X X Y Z ε … Find3
• 25. A. The string: {[()]} … ε { Y X X Y Z ε … Find3
• 26. A. The string: {[()]} … ε { Y X X Y Z ε … Find3
• 27. A. The string: {[()]} … ε Z Y X X Y Z ε … Start
• 28. A. The string: {[()]} … ε Z Y X X Y Z ε … Start
• 29. A. The string: {[()]} … ε Z Y X X Y Z ε … Start
• 30. A. The string: {[()]} … ε Z Y X X Y Z ε … Start
• 31. A. The string: {[()]} … ε Z Y X X Y Z ε … Start
• 32. A. The string: {[()]} … ε Z Y X X Y Z ε … Start
• 33. A. The string: {[()]} … ε Z Y X X Y Z ε … End
• 34. A. The string: {[()]} … ε Z Y X X Y Z ε … End
• 35. A. The string: {[()]} … ε Z Y X X Y Z ε … End
• 36. A. The string: {[()]} … ε Z Y X X Y Z ε … End
• 37. A. The string: {[()]} … ε Z Y X X Y Z ε … End
• 38. A. The string: {[()]} … ε Z Y X X Y Z ε … End
• 39. A. The string: {[()]} … ε Z Y X X Y Z ε … End
• 40. A. The string: {[()]} … ε Z Y X X Y Z ε … Accepted
• 41. B. The string: [{()}] … ε [ { ( ) } ] ε … Start
• 42. B. The string: [{()}] … ε [ { ( ) } ] ε … Start
• 43. B. The string: [{()}] … ε [ { ( ) } ] ε … Start
• 44. B. The string: [{()}] … ε [ { ( ) } ] ε … Start
• 45. B. The string: [{()}] … ε [ { ( X } ] ε … Find1
• 46. B. The string: [{()}] … ε [ { X X } ] ε … Start
• 47. B. The string: [{()}] … ε [ { X X } ] ε … Start
• 48. B. The string: [{()}] … ε [ { X X Z ] ε … Find3
• 49. B. The string: [{()}] … ε [ { X X Z ] ε … Find3
• 50. B. The string: [{()}] … ε [ { X X Z ] ε … Find3
• 51. B. The string: [{()}] … ε [ Z X X Z ] ε … Start
• 52. B. The string: [{()}] … ε [ Z X X Z ] ε … Start
• 53. B. The string: [{()}] … ε [ Z X X Z ] ε … Start
• 54. B. The string: [{()}] … ε [ Z X X Z ] ε … Start
• 55. B. The string: [{()}] … ε [ Z X X Z Y ε … Find2
• 56. B. The string: [{()}] … ε [ Z X X Z Y ε … Rejected (wrong)
• 57. C. The string: {[[()] … ε { [ [ ( ) ] ε … Start
• 58. C. The string: {[[()] … ε { [ [ ( ) ] ε … Start
• 59. C. The string: {[[()] … ε { [ [ ( ) ] ε … Start
• 60. C. The string: {[[()] … ε { [ [ ( ) ] ε … Start
• 61. C. The string: {[[()] … ε { [ [ ( ) ] ε … Start
• 62. C. The string: {[[()] … ε { [ [ ( X ] ε … Find1
• 63. C. The string: {[[()] … ε { [ [ X X ] ε … Start
• 64. C. The string: {[[()] … ε { [ [ X X ] ε … Start
• 65. C. The string: {[[()] … ε { [ [ X X Y ε … Find2
• 66. C. The string: {[[()] … ε { [ [ X X Y ε … Find2
• 67. C. The string: {[[()] … ε { [ [ X X Y ε … Find2
• 68. C. The string: {[[()] … ε { [ Y X X Y ε … Start
• 69. C. The string: {[[()] … ε { [ Y X X Y ε … Start
• 70. C. The string: {[[()] … ε { [ Y X X Y ε … Start
• 71. C. The string: {[[()] … ε { [ Y X X Y ε … Start
• 72. C. The string: {[[()] … ε { [ Y X X Y ε … End
• 73. C. The string: {[[()] … ε { [ Y X X Y ε … End
• 74. C. The string: {[[()] … ε { [ Y X X Y ε … End
• 75. C. The string: {[[()] … ε { [ Y X X Y ε … End
• 76. C. The string: {[[()] … ε { [ Y X X Y ε … End
• 77. C. The string: {[[()] … ε { [ Y X X Y ε … Rejected (unbalanced)
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