I have spent some time looking at the problem of finding a polynomial time solution to logical satisfiability and I have come to a few conclusions about the problem.
There may be a natural solution, but if there is, I certainly can't see it. So if this is at all feasible, a more contrived method needs to be concocted. I believe the solution would have to use an alternative way to compress a logical problem so that individual solutions could be turned out in polynomial time. I can imagine compressing-some- logical formulas that way but I can't think of a general method. But, since it looks like there is no one compression formatting that could be used for every possible logical formula I believe that a solution - if one is feasible - would have to use different compression encryptions for different formulas. The formulas, encoded in one of these yet-to-be-invented compression formats would probably need to contain the encoding methods used to explain how they were encoded, since different formulas (or different classes of formulas) would have to be compressed differently. But, then since a part of logical formula that had been partially expressed in one of these formats would, using this theoretical framework, need to be converted into another compression format for the next part of the formula, that suggests that the compressions would have to be converted into other compressions without fully decompressing them and this compression transformation would have to take place in polynomial time. So one compressed format would have to be transformable into another format as the formula was converted in a step by step fashion. So in conclusion: 1. Different classes of logical formulas would have to be converted into different compression formats and this compression would have to be done efficiently. 2. The new compressed formulas would have to be efficiently readable so, in the worse case, individual solutions could be read out efficiently. 3. The individuated compression formats would have to include something about the encoding used for the formatting. 4. These formats would have to be convertible into another format efficiently in order to process the logical formula in a stepwise fashion. This shows that there are at least 3 different conversion or transformation methods necessary for the new individuated compression methods. An initial analysis of the structure of a logical formula might be used to immediately convert the formula into a different format without going through a step by step conversion- reconversion process. But even if that was possible we would still want to be able to treat logical formulas in a step by step manner. Of course I have no idea if this is even possible. But my next question is whether the inclusion of the compression formatting with the compressed string is inherently too inefficient to be useful.. 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
