Post-Turing Processing

Shawn

Again, one of my rare entries into the Logic and Philosophy of Mathematics section.

Given that everything in Turing Computability is decidable, and hence deterministic, then past states will elucidate future states of a process given enough time. Now, it doesn't seem too hard to post process all the past states of a computable algorithm to have a copy on a hard drive simply reading out what would have to be done by a Central Processing Unit.

Why would one do this? Due to the repetition of large data tasks on something like a mainframe or server, then by post-processing all the information states needed to solve tasks, then I suppose this would drastically shorten the amount of time at solvability of certain tasks. One would in an old concept of computing, be able to parse all the functions needed to process a task on a Post-Turing Processor with such a bedrock of already post-processed information. The only purpose would seem to be a drastically shorter time needed to parallelization of processed tasks with such a file of post-processed information. I doubt you could mount terabytes of information on the cache of the processor; but, maybe an analog chip could do most of the groundwork with such a post-processed file.

My other thoughts are to utilize with such a file a parser on the CPU to read out what tasks would need to the parser to label already computed tasks and by doing this accelerate through tasks in time.

What are your thoughts about this?

fishfry

... have a copy on a hard drive ... — Shawn

Are you perhaps talking about memoization?

In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls to pure functions and returning the cached result when the same inputs occur again. — Wiki

and

A memoized function "remembers" the results corresponding to some set of specific inputs. Subsequent calls with remembered inputs return the remembered result rather than recalculating it, thus eliminating the primary cost of a call with given parameters from all but the first call made to the function with those parameters. — Wiki

Shawn

↪fishfry

Yes, then there's nothing much to further discuss. I did some work on Godel coding for compression algorithms with countable denumerable alphabets, such as color encoding like RGB for satellite TV to deliver true 4,8,12K video. It was a fun task that led me to believe that every denumerable ordered task can be sped up or optimized by actually archiving the read to the CPU with already post-processed information, and thus labeling it as if a "brick" to every further task to be done on similar logic. Eventually, with so many bricks, you could compile the task on the CPU, to just be read out to the memory. To process the information wouldn't be anything too far-fetched; but, the archive file might be quite big to cache. The optimization might be quite profound in my mind.

Is this something that is done already on hardware, or only on software to this day?

fishfry

Yes, then there's nothing much to further discuss. I did some work on Godel coding for compression algorithms with countable denumerable alphabets, such as color encoding like RGB for satellite TV to deliver true 4,8,12K video. It was a fun task that led me to believe that every denumerable ordered task can be sped up or optimized by actually archiving the read to the CPU with already post-processed information, and thus labeling it as if a "brick" to every further task to be done on similar logic. Eventually, with so many bricks, you could compile the task on the CPU, to just be read out to the memory. To process the information wouldn't be anything too far-fetched; but, the archive file might be quite big to cache. The optimization might be quite profound in my mind. — Shawn

I'm not an expert on this topic. As I understand it, memoization is just used to store results of calculations and things like that. I could be wrong because my knowledge is from some years ago.

Your idea seems much more extensive. I would not want my little comment to end this interesting discussion! Your concept seems to go further.

Is this something that is done already on hardware, or only on software to this day? — Shawn

I know it as a software technique, but I'm not up to speed on the state of the art.

wonderer1

Is this something that is done already on hardware, or only on software to this day? — Shawn

At least to an extent, though likely not the extent that you have in mind, a math coprocessor to A CPU provides 'canned math optimization' to CPUs. Although often this is 'hidden' from a programmer, in that the compiler 'knows' how to make use of the coprocessor, and the programmer doesn't need to concern himself with it. (Aside from perhaps understanding that, for example, the combination of hardware and software will be able to produce 32 bit multiplication results in one clock cycle.)

Similar can be pairing a CPU with an FPGA. With such a hardware setup, a wide variety of processes can be designed into the logic fabric of the FPGA (for example a Fast Fourier Transform) so that what would otherwise require a lot of CPU clock cycles can be done much more quickly within the FPGA.

On the technological horizon, are hardware instantiations of artificial neural networks, which will allow memory and processor to be entertwined within each artifical neuron, in such a way that very powerful information processing can occur within the neural network as a whole, which can be faster and much more energy efficient than today's AIs like Chat-GPT.

ssu

Given that everything in Turing Computability is decidable, and hence deterministic, then past states will elucidate future states of a process given enough time.

- What are your thoughts about this? — Shawn

Do remember that Turing's paper is an undecidability result. Not everything is Turing Computable, which would be very useful for us. Hence you are really stretching it when you conclude that "then past states will elucidate future states of a process given enough time".

But how to use already done work on algorithms and not to repeat the work, which @fishfry referred to, is obviously useful.

Post-Turing Processing

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