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NP-Completeness

Comp 750, Fall 2009. NP-completeness - 2. Denoted M = (Q, T, I, ?, b, qo, qf) . Q = finite set of states qo ? Q is start stateT = finite set of tape symbolsqf ? Q is final stateb ? T is blank symbolI = set of input symbols

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NP-Completeness

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    1. Comp 750, Fall 2009 NP-completeness - 1 NP-Completeness

    2. Comp 750, Fall 2009 NP-completeness - 2 Turing Machines

    3. Comp 750, Fall 2009 NP-completeness - 3 Multitape TM

    4. Comp 750, Fall 2009 NP-completeness - 4 Language Accepted by TM

    5. Comp 750, Fall 2009 NP-completeness - 5 Turing Machine - Example

    6. Comp 750, Fall 2009 NP-completeness - 6 Moves

    7. Comp 750, Fall 2009 NP-completeness - 7 Two Move Sequences

    8. Comp 750, Fall 2009 NP-completeness - 8 Complexity

    9. Comp 750, Fall 2009 NP-completeness - 9 Deterministic vs. Nondeterministic

    10. Comp 750, Fall 2009 NP-completeness - 10 Behavior of M2

    11. Comp 750, Fall 2009 NP-completeness - 11 (Non)determinism and Time Complexity

    12. Comp 750, Fall 2009 NP-completeness - 12 Single-Tape vs. Multi-Tape

    13. Comp 750, Fall 2009 NP-completeness - 13 Problems and Languages

    14. Comp 750, Fall 2009 NP-completeness - 14 Example

    15. Comp 750, Fall 2009 NP-completeness - 15 Problem Encodings

    16. Comp 750, Fall 2009 NP-completeness - 16 Non-(yes/no) Problems

    17. Comp 750, Fall 2009 NP-completeness - 17 Four Basic Complexity Classes

    18. Comp 750, Fall 2009 NP-completeness - 18 Relationships

    19. Comp 750, Fall 2009 NP-completeness - 19 P-Space = NP-Space

    20. Comp 750, Fall 2009 NP-completeness - 20 Proof (Continued)

    21. Comp 750, Fall 2009 NP-completeness - 21 DTM That Simulates M

    22. Comp 750, Fall 2009 NP-completeness - 22 NP-Time ? P-Space

    23. Comp 750, Fall 2009 NP-completeness - 23 P-Time ? NP-Time

    24. Comp 750, Fall 2009 NP-completeness - 24 One more Class: co-NP

    25. Comp 750, Fall 2009 NP-completeness - 25 Relationship between co-NP & P-Space

    26. Comp 750, Fall 2009 NP-completeness - 26 Why do we care about co-NP?

    27. Comp 750, Fall 2009 NP-completeness - 27 Real-Time Scheduling Problem

    28. Comp 750, Fall 2009 NP-completeness - 28 P vs. NP

    29. Comp 750, Fall 2009 NP-completeness - 29 Hard and Complete Problems

    30. Comp 750, Fall 2009 NP-completeness - 30 NP-Complete Problems

    31. Comp 750, Fall 2009 NP-completeness - 31 NP-Complete Problems (Continued)

    32. Comp 750, Fall 2009 NP-completeness - 32 Doing it from Scratch: Cooks Thm

    33. Comp 750, Fall 2009 NP-completeness - 33 Setting Up the Proof

    34. Comp 750, Fall 2009 NP-completeness - 34 Setting Up the Proof (Continued)

    35. Comp 750, Fall 2009 NP-completeness - 35 Construction of Expression w0

    36. Comp 750, Fall 2009 NP-completeness - 36 Construction of Expression w0 (Continued)

    37. Comp 750, Fall 2009 NP-completeness - 37 Variables in w0

    38. Comp 750, Fall 2009 NP-completeness - 38 Main Proof Obligation

    39. Comp 750, Fall 2009 NP-completeness - 39 Claim (Continued)

    40. Comp 750, Fall 2009 NP-completeness - 40 Claim (Continued)

    41. Comp 750, Fall 2009 NP-completeness - 41 Claim (Continued)

    42. Comp 750, Fall 2009 NP-completeness - 42 Claim (Continued)

    43. Comp 750, Fall 2009 NP-completeness - 43 Claim (Continued)

    44. Comp 750, Fall 2009 NP-completeness - 44 Time Complexity

    45. Comp 750, Fall 2009 NP-completeness - 45 Cooks Theorem Example

    46. Comp 750, Fall 2009 NP-completeness - 46 Example (Continued)

    47. Comp 750, Fall 2009 NP-completeness - 47 Example (Continued)

    48. Comp 750, Fall 2009 NP-completeness - 48 Example (Continued)

    49. Comp 750, Fall 2009 NP-completeness - 49 Example (Continued)

    50. Comp 750, Fall 2009 NP-completeness - 50 Variations on Satisfiability

    51. Comp 750, Fall 2009 NP-completeness - 51 CNF Satisfiability

    52. Comp 750, Fall 2009 NP-completeness - 52 3-Sat

    53. Comp 750, Fall 2009 NP-completeness - 53 3-Sat (Continued)

    54. Comp 750, Fall 2009 NP-completeness - 54 Problems We Consider

    55. Comp 750, Fall 2009 NP-completeness - 55 Clique

    56. Comp 750, Fall 2009 NP-completeness - 56 Clique (Continued)

    57. Comp 750, Fall 2009 NP-completeness - 57 Clique (Continued)

    58. Comp 750, Fall 2009 NP-completeness - 58 Vertex Cover

    59. Comp 750, Fall 2009 NP-completeness - 59 Vertex Cover (Continued)

    60. Comp 750, Fall 2009 NP-completeness - 60 Vertex Cover (Continued)

    61. Comp 750, Fall 2009 NP-completeness - 61 Feedback Vertex Set

    62. Comp 750, Fall 2009 NP-completeness - 62 Feedback Edge Set

    63. Comp 750, Fall 2009 NP-completeness - 63 Feedback Edge Set (Continued)

    64. Comp 750, Fall 2009 NP-completeness - 64 Directed Hamilton Circuit

    65. Comp 750, Fall 2009 NP-completeness - 65 DHC (Continued)

    66. Comp 750, Fall 2009 NP-completeness - 66 DHC (Continued)

    67. Comp 750, Fall 2009 NP-completeness - 67 Example

    68. Comp 750, Fall 2009 NP-completeness - 68 DHC (Continued)

    69. Comp 750, Fall 2009 NP-completeness - 69 Example

    70. Comp 750, Fall 2009 NP-completeness - 70 DHC (Continued)

    71. Comp 750, Fall 2009 NP-completeness - 71 Example

    72. Comp 750, Fall 2009 NP-completeness - 72 DHC (Continued)

    73. Comp 750, Fall 2009 NP-completeness - 73 DHC (Continued)

    74. Comp 750, Fall 2009 NP-completeness - 74 DHC (Continued)

    75. Comp 750, Fall 2009 NP-completeness - 75 Hamilton Circuit Problem

    76. Comp 750, Fall 2009 NP-completeness - 76 HCP (Continued)

    77. Comp 750, Fall 2009 NP-completeness - 77 HCP (Continued)

    78. Comp 750, Fall 2009 NP-completeness - 78 Set Cover Problem

    79. Comp 750, Fall 2009 NP-completeness - 79 Colorability

    80. Comp 750, Fall 2009 NP-completeness - 80 Colorability

    81. Comp 750, Fall 2009 NP-completeness - 81 Colorability (Continued)

    82. Comp 750, Fall 2009 NP-completeness - 82 Coloring G

    83. Comp 750, Fall 2009 NP-completeness - 83 Coloring the Fjs

    84. Comp 750, Fall 2009 NP-completeness - 84 Colorability

    85. Comp 750, Fall 2009 NP-completeness - 85 Exact Cover

    86. Comp 750, Fall 2009 NP-completeness - 86 Exact Cover (Continued)

    87. Comp 750, Fall 2009 NP-completeness - 87 Exact Cover (Continued)

    88. Comp 750, Fall 2009 NP-completeness - 88 Exact Cover (Continued)

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