Quote from: gjhiggins on August 22, 2015, 05:30:05 PM

CIYAM's "specification" document is wrong as well as imprecise, ATs in themselves are not Turing complete and scarequotes won't make it so.

Please point out exactly (technically) what is wrong as well as imprecise as just saying that something is *wrong as well as imprecise* doesn't make it so.

The AT machine code supports jumping, subroutines, stacks, conditional logic and memory and this is enough to be able to run "any program" in the sense that you could write a C++ compiler with the AT "virtual CPU" as its platform (I assume you are not going to deny that C++ is "Turing complete") and in fact that is one of the potential projects being considered (although we do not have millions of dollars in funding to pay for such work at this stage).

If you haven't read so please check this: https://en.wikipedia.org/wiki/One_instruction_set_computer and you'll learn that it is so "easy to be Turing complete" that even a "single op code" machine can be so. Basically Bitcoin's Script was intentionally built to not be "Turing complete" as it is actually harder to do that (is has several special checks to make sure it can't accidentally end up looping and numerous op codes were actually removed due to their potential to cause trouble).

There is no "special magic sauce" required in order to be "Turing complete" but just the ability to have conditional logic, variables and loops (all of which AT has).

If you think that a mathematical proof of being "Turing complete" is needed then please show me where Ethereum have provided this and I'll get a math guy to write an equivalent document for AT.

When you read the specs of any CPU it doesn't come with a mathematical proof about being "Turing complete" but instead looks just like the specification that was created for AT (i.e. documenting the instruction set and other key features such as word size, etc.).

So how on earth can we ever create "Turing complete" programs if we are using compilers and interpreters that are running on "Turing incomplete" CPUs? Roll Eyes