1. The Off-Line Machine Input File read-only (once) Input string
Appears on
input file only
Input string
Control Unit
(state machine)
Tape
read-write
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2. have the same power with Standard Turing machines
Theorem:
Off-Line machines
have the same power with
Standard Turing machines
Proof:
1. Off-Line machines
simulate Standard Turing machines 2.
Standard Turing machines
simulate Off-Line machines
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3. 1. Off-line machines simulate Standard Turing Machines
1. Copy input file to tape
2. Continue computation as in
Standard Turing machine
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4. Standard machine Off-line machine Tape Input File
1. Copy input file to tape
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5. 2. Do computations as in Turing machine
Standard machine
Off-line machine
Tape
Input File
2. Do computations as in Turing machine
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6. 2. Standard Turing machines simulate Off-Line machines:
Use a Standard machine with
a four-track tape to keep track of
the Off-line input file and tape contents
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7. Standard Machine -- Four track tape
Off-line Machine
Tape
Input File
Standard Machine -- Four track tape
Input File
head position
Tape
head position
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8. Repeat for each state transition: Return to reference point
(uses special symbol # )
Input File
head position
Tape
head position
Repeat for each state transition:
Return to reference point
Find current input file symbol
Find current tape symbol
Make transition
END OF PROOF
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