TM_multitape

Transcript

1. Multi-tape TM
   0: t 0 0 0 1 + 1 0 0 1 = 1 0 1 0 t
   1: t t t t t t t t t t t t t t t t
   2: t t t t t t t t t t t t t t t t
   We start with input on tape 0. Other tapes are blank.
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2. Multi-tape TM
   0: t t t t t + 1 0 0 1 = 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t t t t t t t t t t t t t t t t
   We can copy the first operand to tape 1, crossing it off as we go
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3. Multi-tape TM
   0: t t t t t t t t t t = 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t 1 0 0 1 t t t t t t t t t t t
   We can copy the second operand to tape 2, crossing it off as
   we go
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4. Multi-tape TM
   0: t t t t t t t t t t t 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t 1 0 0 1 t t t t t t t t t t t
   We scan to the end
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5. Multi-tape TM
   0: t t t t t t t t t t t 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t 1 0 0 1 t t t t t t t t t t t
   Move left once on all tapes, and then just check each digit one
   by one, moving left. Remember carry in state.
   Carry in = 0
   Carry out = 1
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6. Multi-tape TM
   0: t t t t t t t t t t t 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t 1 0 0 1 t t t t t t t t t t t
   Carry in = 1
   Carry out = 0
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7. Multi-tape TM
   0: t t t t t t t t t t t 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t 1 0 0 1 t t t t t t t t t t t
   Carry in = 0
   Carry out = 0
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8. Multi-tape TM
   0: t t t t t t t t t t t 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t 1 0 0 1 t t t t t t t t t t t
   Carry in = 0
   Carry out = 0
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9. Multi-tape TM
   0: t t t t t t t t t t t 1 0 1 0 t
   1: t 0 0 0 1 t t t t t t t t t t t
   2: t 1 0 0 1 t t t t t t t t t t t
   Carry in = 0
   All tapes on t
   Accept!
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