A functional method is (can be) both a compression method and an algebraic method. Since a functional method could effectively act like an enumeration of different kinds of functions over the system, it could be used to derive a log-complex solution method over the system. And since the problem of logical satisfiability uses an effective compression over the system as the input to the solver it might be possible to develop a functional representation that would still retain the log-complexity relation of logical formulas to the final output.
And a functional method does show the compression mechanisms that are being used in the representation. (A compressed form does not have to explicitly show anything about the methods used in the compression although this might lead to an intangible question in itself.) I believe it would be easy to develop methods that would work (in polynomial time) for simpler formulas. And, the superficial representations of the functions do not have to be tied *directly* to the superficial representations of traditional logical methods. So the question then is: can these systems be extended for more complicated formulas as needed? It might be possible to design new functions as needed. Of course the functions can be extended as needed. (In other words, not only can the variables of the input to these functions be extended, the functions also can be extended.) But, exotic new functions might also need to be created. Ironically, if my current conjecture is correct then this could mean that the theory could continue to be extended after my death similar to Ben's joke about me minus "the Singularity" and "uploading" nonsense. Here, the question is whether new classes of function-generators (that operate on new classes of the problem) can be created in the same way as new numerical theories have been created? It seems like a very reasonable conjecture to me. To help you see this, stop thinking of the satisfiability problem as it is in p or not. (If a solver can't act in polynomial time for every possible problem then it is not in p). Start thinking of the problem as a question of the proportion of logical problems of length n that can be solved in polynomial time. Imagine that an extensive random walk was done on logical problems and this data was then used to map this proportion onto an equation for the length of n. What are you going to find? As n increases the proportion of problems that cannot be solved in polynomial time is going to increase. I don't think this increase even has to be exponential to make my case, but I am almost sure it would be. At any rate, from this point of view, it would show that as new theories about the function-generator are developed the range and proportion of problems that can be solved in polynomial time will increase. So it is up to me to show that the basic premise is correct and find an algebraic functional method that will work in polynomial time for greater input lengths than is currently possible, even if it does not work in polynomial time for all problems of any length. Jim Bromer On Mon, Jun 16, 2014 at 9:04 AM, Ben Goertzel via AGI <[email protected]> wrote: > > Hmm...well, some folks believe one could create a future upload of a > physically deceased human via analysis of their online texts... remember > Giulio Prisco's idea of Mind Uploading via Gmail... > > http://giulioprisco.blogspot.hk/2010/09/mind-uploading-via-gmail.html > > Maybe, post-Singularity, Jim Bromer's upload will find a polynomial time > solution to 3SAT? > > > ;-) > ben > > > > On Mon, Jun 16, 2014 at 8:55 PM, Anastasios Tsiolakidis < > [email protected]> wrote: > >> Shame on you Ben, again! He Creative Commons licensed his mind, that's >> why. >> >> AT >> >> On 16.06.2014, at 14:52, "Ben Goertzel via AGI" <[email protected]> wrote: >> >> >> I wonder why you enjoy talking to yourself on a public email list? ;-) >> >> >> On Mon, Jun 16, 2014 at 8:48 PM, Jim Bromer via AGI <[email protected]> >> wrote: >> >>> 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> >>> <https://www.listbox.com/member/archive/rss/303/212726-deec6279> | >>> Modify <https://www.listbox.com/member/?&;> Your Subscription >>> <http://www.listbox.com> >>> >> >> >> >> -- >> Ben Goertzel, PhD >> http://goertzel.org >> >> "In an insane world, the sane man must appear to be insane". -- Capt. >> James T. Kirk >> >> "Emancipate yourself from mental slavery / None but ourselves can free >> our minds" -- Robert Nesta Marley >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/14050631-7d925eb1> | >> Modify <https://www.listbox.com/member/?&;> Your Subscription >> <http://www.listbox.com> >> >> > > > -- > Ben Goertzel, PhD > http://goertzel.org > > "In an insane world, the sane man must appear to be insane". -- Capt. > James T. Kirk > > "Emancipate yourself from mental slavery / None but ourselves can free our > minds" -- Robert Nesta Marley > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/24379807-f5817f28> | > Modify > <https://www.listbox.com/member/?&;> > Your Subscription <http://www.listbox.com> > ------------------------------------------- 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
