Question

If you take the original Turing machine definition as follows:

…an infinite memory capacity
obtained in the form of an infinite
tape marked out
into squares, on each of which a symbol could be printed. At any moment
there is
one symbol in the machine; it is called the scanned symbol. The machine
can alter
the scanned symbol and its behavior is in part determined by that
symbol, but the
symbols on the tape elsewhere do not affect the behavior of the
machine. However,
the tape can be moved back and forth through the machine, this being
one of the
elementary operations of the machine. Any symbol on the tape may
therefore
eventually have an innings. (Turing 1948, p. 61)

If you want to map these operations to those done on a processor capable of interpreting assembler/binary instructions – which operations would be mapped?

(I’m aware of the jump from Turing machines to Von Neuman machines inherent in this question)

Answer 1

Reading what you’ve written I’d say you just need:

• A direct increment instruction (to add to the current tape location)
• An indirect increment instruction (to move the tape)
• Something to act in response of the current tape location value

In an ARM-like assembly, for example, if you have R0 containing the address on the tape you should just need

ADDS r0, r0, #1 ;moves the tape forward
ADDS r0, r0, #-1 ;moves the tape backwards
ADDS [r0], [r0], #1 ;increments the value 'pointed by' the tape
ADDS [r0], [r0], #-1 ;decrements the value 'pointed by' the tape

Then, branches to do stuff in case of certain values assumed by the current symbol

BEQ Somewhere

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