complexity recitation 2

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Complexity Recitation 2

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Complexity Recitation 2. k-Tape Turing Machines. k-Tape Turing Machines. k-Tape Turing Machines. k-Tape Turing Machines. k-Tape Turing Machines. Log Space Turing Machines. Diagonalization. Diagonalization. Diagonalization. Diagonalization. Diagonalization. Diagonalization. - PowerPoint PPT Presentation

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Page 1: Complexity Recitation 2

ComplexityRecitation 2

Page 2: Complexity Recitation 2

2

k-Tape Turing Machines

Page 3: Complexity Recitation 2

3

k-Tape Turing Machines

Page 4: Complexity Recitation 2

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k-Tape Turing Machines

Page 5: Complexity Recitation 2

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k-Tape Turing Machines

Page 6: Complexity Recitation 2

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k-Tape Turing Machines

Page 7: Complexity Recitation 2

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Log Space Turing Machines

Page 8: Complexity Recitation 2

8

Diagonalization

Page 9: Complexity Recitation 2

… L(M6) L(M5) L(M4) L(M3) L(M2) L(M1) Lang

Input

<M1>

<M2>

<M3>

<M4>

<M5>

<M6>

Diagonalization

Page 10: Complexity Recitation 2

… L(M6) L(M5) L(M4) L(M3) L(M2) L(M1) Lang

Input

... X X V V X V <M1>

... V V V V X V <M2>

... X V X V X V <M3>

... V X V V V X <M4>

... V X X V X X <M5>

... X X X V V V <M6>

... …

Diagonalization

Page 11: Complexity Recitation 2

… L(M6) L(M5) L(M4) L(M3) L(M2) L(M1) Lang

Input

... X X V V X V <M1>

... V V V V X V <M2>

... X V X V X V <M3>

... V X V V V X <M4>

... V X X V X X <M5>

... X X X V V V <M6>

... …

Diagonalization

Page 12: Complexity Recitation 2

L(M) … L(M6) L(M5) L(M4) L(M3) L(M2) L(M1) Lang

Input

X ... X X V V X V <M1>

V ... V V V V X V <M2>

X ... X V X V X V <M3>

X ... V X V V V X <M4>

V ... V X X V X X <M5>

V ... X X X V V V <M6>

... …

Diagonalization

Page 13: Complexity Recitation 2

L(M) … L(M6) L(M5) L(M4) L(M3) L(M2) L(M1) Lang

Input

X ... X X V V X V <M1>,c1

V ... V V V V X V <M2>,c2

X ... X V X V X V <M3>,c3

X ... V X V V V X <M4>,c4

V ... V X X V X X <M5>,c5

V ... X X X V V V <M6>,c6

... …

Diagonalization

Page 14: Complexity Recitation 2

L(M) … L(M6) L(M5) L(M4) L(M3) L(M2) L(M1) Lang

Input

X ... X X V V X V <M1>,1^c1

V ... V V V V X V <M2>,1^c2

X ... X V X V X V <M3>,1^c3

X ... V X V V V X <M4>,1^c4

V ... V X X V X X <M5>,1^c5

V ... X X X V V V <M6>,1^c6

... …

Diagonalization

Page 15: Complexity Recitation 2

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Diagonalization

Page 16: Complexity Recitation 2

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Diagonalization

Page 17: Complexity Recitation 2

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Diagonalization

Page 18: Complexity Recitation 2

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coNP

Page 19: Complexity Recitation 2

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coNP

Page 20: Complexity Recitation 2

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coNP

Page 21: Complexity Recitation 2

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coNP

Page 22: Complexity Recitation 2

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coNP

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coNP