# Complexity Recitation 2 kTape Turing Machines kTape Turing

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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 Lang L(M 1) Input <M 1> <M 2> <M 3> <M 4> <M 5> <M 6> … L(M 2) L(M 3) L(M 4) L(M 5) L(M 6) …

Diagonalization Lang L(M 1) L(M 2) L(M 3) L(M 4) L(M 5) L(M 6) … <M 1> V X V V X X . . . <M 2> V X V V . . . <M 3> V X V X . . . <M 4> X V V V X V . . . <M 5> X X V . . . <M 6> V V V X X X . . . Input … . . .

Diagonalization Lang L(M 1) L(M 2) L(M 3) L(M 4) L(M 5) L(M 6) … <M 1> V X V V X X . . . <M 2> V X V V . . . <M 3> V X V X . . . <M 4> X V V V X V . . . <M 5> X X V . . . <M 6> V V V X X X . . . Input … . . .

Diagonalization Lang L(M 1) L(M 2) L(M 3) L(M 4) L(M 5) L(M 6) … L(M) <M 1> V X V V X X . . . X <M 2> V X V V . . . V <M 3> V X V X . . . X <M 4> X V V V X V . . . X <M 5> X X V . . . V <M 6> V V V X X X . . . V Input … . . .

Diagonalization Lang L(M 1) L(M 2) L(M 3) L(M 4) L(M 5) L(M 6) … L(M) <M 1>, c 1 V X V V X X . . . X <M 2>, c 2 V X V V . . . V <M 3>, c 3 V X V X . . . X <M 4>, c 4 X V V V X V . . . X <M 5>, c 5 X X V . . . V <M 6>, c 6 V V V X X X . . . V Input … . . .

Diagonalization Lang L(M 1) L(M 2) L(M 3) L(M 4) L(M 5) L(M 6) … L(M) <M 1>, 1^c 1 V X V V X X . . . X <M 2>, 1^c 2 V X V V . . . V <M 3>, 1^c 3 V X V X . . . X <M 4>, 1^c 4 X V V V X V . . . X <M 5>, 1^c 5 X X V . . . V <M 6>, 1^c 6 V V V X X X . . . V Input … . . .

Diagonalization

Diagonalization

Diagonalization

co. NP

co. NP

co. NP

co. NP

co. NP

co. NP