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Not quite, in practice they are pretty much equivalent but they're not Universal Turing Machines. For that they would need to have infinite memory. A Universal
by almost 17y ago
Not quite, in practice they are pretty much equivalent but they're not Universal Turing Machines. For that they would need to have infinite memory. A Universal Turing Machine is a theoretical construct, it's not something that could actually exist.
- jvdh 17y agoI did some more research and digging through my books. A Universal Turing machine is one that can read programs from its own tape. Infinite tapes are necessary for the halting problem, to allow programs to run infintely on infinite memory. Turing Completeness is when the machine is proven to be equivalent to a Turing Machine, i.e. it can be programmed to solve any algorithmical problem.
- almost 17y agoYour definition is slightly wrong. In Alan Turing's own words: It is possible to invent a single machine which can be used to compute any computable sequence. If this machine I is supplied with a tape on the beginning of which is written the S.D of some computing machine M, {242} then I will compute the same sequence as M. (Alan Turing, 1936, On Computable Numbers, With An Application To The Entscheidungsproblem) So it is no merely that the Universal Machine can read and execute programs, it is that it can read and executes programs to make itself equivalent to ANY other turing machine. Thus the Universal Turing machine is Turing Complete. As the amount of tape required to solve all computable programs is unbounded the Universal Turing machine must have an infinitely long tape. It's usually worth going straight to the source where you can in CS, but much more so with Turing as his papers are so nice and easy to read :)