Jim, I assume you are you familiar with https://en.wikipedia.org/wiki/P_versus_NP_problem and why it is relevant to your problem. Have you tried solving other NP-complete problems like subset-sum or traveling salesman as a path to SAT?
On Wed, Jul 10, 2013 at 10:00 AM, Jim Bromer <[email protected]> wrote: > Matt, > I have done very little research other than reading about it on the > Internet. I have come across examples in various mathematic text books and > so on as I was studying logic and other cs/mathematic books. I did read > one more specialized book at one point but I was not too excited by it. > > For example, I am not interested in stochastic methods for the obvious > reasons. I just cannot see how a probability method could possibly lead to > a deterministic result without being dependent on deterministic methods. > Having said that I do keep thinking about using a method of fuzzy logic > which I derived personally which is based on the number of known true and > false lines. I would use the method to narrow down the possibilities. > However, the fuzzy logic (which I sometimes see in my partial derivations) > is not a substitute for discovering the way to define a viable path to > narrow those possibilities. > > As you probably remember, part of my study was to see if I could use > this tremendous challenge as rational evidence to support my momentary > belief that I had received some guidance on the problem from the Lord back > in 2007. So I am not pursuing a more academic study of methods that have > been tried and which have led to some advances in the past because they > probably wouldn't help me and they would probably interfere with > the development of my own personal methods. And I just do not see the > value in building on methods which are proven to be too weak. I realize > that there are some exceptions of course, but wading through tons of > information to find an ounce of gold is not my idea of a worthwhile effort. > > As you guessed some time ago, I have been working on methods which use the > number of true and false lines for each unique variable (or literal) for a > formula. I found a way to keep track of the evaluation of those numbers > as my algorithm 'read' a simple formula. It was very difficult for me to > figure out how to do this since the formula keeps dividing the results > into two groups and then conditionally recombine them (in a simple > formula). So once I figured it out I was very excited that it did work. > But when I tried to evaluate two sub-compound formulas where some of the > variables appeared on either side of the operation I discovered that the > count of the number of true and false lines that each variable appeared > in was lossy. You could have the same count for different simple > formulas. And there were other problems. Even though I could figure out a > way to use this method with an operation on two simple logical formulas, I > found that keeping track of the intermediate results using the method I > came up with was in np. > > So I have been trying to find a way to use a combination > of compression methods to represent the intermediate results and which > could be used in the evaluation process as well. I have tried to imagine > how such a thing might work for a simpler example but I never made much > progress. I mentioned sometime ago that the n-ary system of > representation, where n>1 was an amazing compression method which can be > used for both the representation of a number and for calculations. Some > people did not get what I was saying, but the fundamental method of > representing and counting is not a binary or decimal system but a unitary > method. When you compare the agility of binary or decimal system operations > against the plodding methods of unitary calculations the lopsided advances > of sciences that can be adequately represented using fundamental operations > on numerical values becomes clear. > > This is a sound basis for a research path. Although a de-emphasis of the > academic approach may not be advisable in general it is a fact that > innovation has to rely on individuation. So a general plan has to include > some leeway for outliers. And I have been exposed to a number of basic > sources on the problem so it is not like I am living in the middle ages or > something. > > Jim Bromer > > > ------------------------------ > Date: Sun, 7 Jul 2013 20:45:46 -0400 > Subject: Re: [agi] I am working on another possible DPT solution to > logical satisfiability > From: [email protected] > To: [email protected] > > Jim, what research have you done on the problem? I don't mean searching > for solutions on your own. I mean reading papers on the P vs. NP problem > and the background mathematics. > > > On Sun, Jul 7, 2013 at 5:32 PM, Jim Bromer <[email protected]> wrote: > > I recently mentioned that I thought I had a deterministic polynomial > time 3-SAT solution that might work. I did not find a counter-example but > I am pretty sure that it would not have worked. However, I am now working > on another solution to SAT and I think this is the best one that I have had > so far. > There are two things that are interesting about my current effort. It is > a solution that is closest to what I was thinking of on the day when I > thought that the Lord may have had told me (indirectly) that I had found a > solution path for the problem. For some reason I did not put all the > pieces together until a few days ago. So, from the perspective of a > motivation from faith this current solution looks like it might be the best > one I have had yet. The second thing that is interesting about this > current solution is that I have made a surprising new discovery that I > hadn't seen before. > Jim Bromer > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/3701026-786a0853> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > > > > > -- > -- Matt Mahoney, [email protected] > *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> > <https://www.listbox.com/member/archive/rss/303/3701026-786a0853> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- -- Matt Mahoney, [email protected] ------------------------------------------- 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
