turing machine :(

[newuser]

im having difficulty in understanding turing machines if anyone can help can they explain to me the following:-
a turing machine starts off with its read/write head at the leftmost bit of the binary representation of an arbitary numbern, and terminates with its read/write head at the leftmost bit of the binary representation of n + 1.
thanks in advance

[kedaman]

Which part doesn't make sense?
A turing machine is a state automaton that operates on an infinite tape with a finite amount of symbols, in a finite alphabet, according to a finite instruction set, having a finite amount of states. Each instruction is a cartesian product of these elements:
input symbol (which is read from the tape)
output symbol (which is written to the tape)
the state in which the instruction executes
the consequent state.
Right/Left (depending on which direction on the tape the read/write head will move)
a binary representation of a number, is a number written using only two digits, 0 and 1, where digit n is the number/2^(n-1) modulus 2.

[Guv]

I think a Turing machine can only do a few operations (less than 10-20). Try a Web search to find out what operations are allowed. It should be a lot simpler to understand than the posted description of this hypothetical device.

Turing proved that his simple machine could do anything that more complicated machines could do. Since it was easier to analyze than a complex device, it could be used to determine the theoretical capabilities of more complex systems.

[wossname]

Turing machines are cool but they are very hard to program.

[kedaman]

I think a Turing machine can only do a few operations (less than 10-20). Try a Web search to find out what operations are allowed. It should be a lot simpler to understand than the posted description of this hypothetical device.

Turing proved that his simple machine could do anything that more complicated machines could do. Since it was easier to analyze than a complex device, it could be used to determine the theoretical capabilities of more complex systems.

10-20, where did you get that number?
There should only be one kind of instruction, which looks like this:
(StateA, StateB, Read, Write, Direction)

For instance, if I have a tape looking like this:

[..A,B,C,D..]

the head is on B, and the TM is in state X,

and we have this instruction:

(X,Y,B,E,Right)

then what follows is

[..A,E,C,D..]

the head is now on C, and the TM is in state Y.

[dglienna]

Six operations are allowed.

* read (i.e. identify) the symbol currently under the head
* write a symbol on the square currently under the head (after first deleting the symbol already written there, if any)
* move the tape left one square
* move the tape right one square
* change state
* halt.

http://www.alanturing.net/turing_arc...20Machine.html

[kedaman]

yeah ok, if thats what you mean by operation.. but then again you could have so many more operations...