I have tried those problems and I have read a few Wikipedia entries related to the subject. Subset sum is a good problem because it is so basic but I am not sure that as basic as SAT. Date: Wed, 10 Jul 2013 10:52:20 -0400 Subject: Re: [agi] I am working on another possible DPT solution to logical satisfiability From: [email protected] To: [email protected]
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. 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