Turing machine

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

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

18. A. The string: {[()]} … ε { Y X X Y } ε … Start

22. A. The string: {[()]} … ε { Y X X Y Z ε … Find3

27. 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

40. A. The string: {[()]} … ε Z Y X X Y Z ε … Accepted

41. 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

51. 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

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

68. C. The string: {[[()] … ε { [ Y X X Y ε … Start

72. C. The string: {[[()] … ε { [ Y X X Y ε … End

77. C. The string: {[[()] … ε { [ Y X X Y ε … Rejected (unbalanced)

Turing machine

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Turing machine