Jim Bromer
On Sat, Jun 14, 2014 at 9:20 PM, Jim Bromer <[email protected]> wrote: > 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
