The Halting Problem shows that the results of programs (programmable logic) cannot be completely computed - for every possible program - without running the program. (The Gödel Incompleteness Theorem shows that there are -some- comprehendible logical problems that could not even be theoretically resolved programmatically.)
But there are some programs that can be computationally processed so that a system of results can be produced more quickly than actually running the program. The significance of this came to me after I started criticizing the proposition that an advanced representational compression could be sufficient to produce AGI at this time. The problem is that representational compressions have to go through stages of decompression and recompression in order to do any computation on the data, and given the degree of compression that would be needed for AGI that would make the system way too slow. While logical computation is a simple process using binary representations of simple logical states for each literal (logical variable), the problem is that logical Satisfiability statements are (most familiarly) compressions of multiple logical states. A logical statement is (typically) a compression of a system of individual 'solutions'. So what would be needed would be a computational method that can act efficiently on a wide variety of logical solutions. In other words we need a compression method which can do computations on the compressed representations without (excessively) decompressing them for each computation. I started thinking about this project from the view that my goal is not to make p=np but to try to develop a methodology that might one day be more efficient than methods that we currently use. I started thinking that it might be possible to create compression representations that acted from different levels of abstraction. These levels of abstraction might be thought of as programs. I started thinking about Turing's Halting Problem and I realized that while you cannot find a shortcut to the completion state of every possible computer program, you can for some kinds of programs. The results of a system that I am imagining could be decompressed (at the end of the analytical computational stages) to produce solutions using the levels-of-abstraction sub-program. but the system could run through the computational steps without actually running that sub-program. The compressed representations would not have to be excessively decompressed in order to run a computation on them. I am all but certain that an example is feasible (although I do not have one right now). And incidentally, an advancement that shows that a compression system might be accompanied by an effective computational method that can act on the compressed representations without fully decompressing them might be interesting to some people. The system does not have to beat Turing at run-around-the-house chess or to prove Gödel wrong from under a table at a week-long Oktoberfest or be dependent on winning a million dollars, it only has to be interesting, incrementally improvable and salient to the study of logic. Jim Bromer ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
