>> 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..
Presuming that different classes of logical formulas could be compressed in different ways, is it possible to use a single polynomial time algorithm to do this? It might be possible, for example, using a numerical method to choose an algorithm based on a numbering system (where an ordering of algorithms might, to continue with this conjectural example, be associated with a log-based number - an n-ary number - to choose the algorithm from a system of algorithms which are in their entirety in np). This is too complicated for me, but if the parts of the algorithms were ordered and enumerated then large numbers could be used to refer to a particular ordering scheme. I am just trying to establish that there could be a way to express variations in how a compression conversion method might be chosen even if the entire list of algorithms were themselves in np. But, is a compression method which includes some way to describe or refer to the particular compression scheme used in the compression going to be so much less efficient than a system that leaves that kind of information out to make this whole idea theoretically impossible? I think that it is theoretically possible. Jim Bromer On Sun, Jun 15, 2014 at 8:20 AM, Jim Bromer <[email protected]> wrote: > > > 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
