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
