Příspěvky

Will trilinear logic help with the completeness obstacle?

In the previous blogpost , we have seen that the poset-linear logic is not refutation complete for certain theories in it. This is a major obstacle in building a (possibly polynomial) algorithm that decides satisfiability problem by constructing the set of tautologies, as I explained there. Here I discuss my plan to fix this problem, which is to build a larger logic (I will call it trilinear), and try to show refutation completeness of all theories of poset-linear logic within trilinear logic. Despite trilinear logic being larger, it's only slightly so, and hopefully it will not present an obstacle for the step 3 of the grand strategy. Trilinear Logic So let's start with definition of the new trilinear deductive system TL. The formulas are going to be expressions αβγ, where α,β,γ are (as usual) any generalized literals. The generalized literals are essentially linear equations over Z2, and for variables $x_1,\ldots...

My current strategy to prove P=NP

Since I have already opened up about my intent and strategy to prove P=NP in some HN comments ( https://news.ycombinator.com/item?id=36082578 and https://news.ycombinator.com/item?id=35729626 ), I decided I should explain it in a series of posts. After all, this was my original goal when I started the blog, to explain more the exciting possibility that P=NP (with a nice constructive algorithm), so that more people could get involved and contribute to that approach. As for my motivation, that's probably a topic for another blog post, let's just say I think it is an extremely important problem to work on. I have been working on understanding P vs NP question as a serious hobby for about 6 years now, however, it was a discovery I made about a year ago that made me really optimistic about P=NP, and that a proof can be close. (Up to that point, I was always trying to be agnostic about the question, although I do admit I don't really buy many arguments or intuitions for P!=NP, a...

A new SAT solving algorithm

 Hello, I am interested in P vs NP and other complexity questions. For now, there is a new SAT solving algorithm that you can read about: pldecomposition.pdf  Update: The above paper has a slight bug in rare cases, although the safe choice conjecture might still hold. Consider it retracted. I will post an updated version.