I am probably wrong. The solution to finding a solution to a logical satisfiability problem in polynomial time is probably going to be based on a natural solution that does an accounting of the number of solutions to the logical problem.
Jim Bromer On Sun, Jun 15, 2014 at 9:05 AM, Jim Bromer <[email protected]> wrote: > Traditional logic is a compressed format. Since there are so many possible > equivalences we know that logic is not a perfectly packed compression > method. So there is no need for a list of alternative compression > conversion algorithms which were in a list of possible algorithms that was > in np. (I expressed that idea incorrectly. I should have talked about a > list of possible algorithms which were in exp space or something like that. > If the list of possible compression-conversion algorithms were in np then > that implies that finding an algorithm solution might itself be in np.) > > > > Jim Bromer > > > On Sun, Jun 15, 2014 at 8:36 AM, Jim Bromer <[email protected]> wrote: > >> >> 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
