A method using flow networks with costs to realize logical gates. This would suggest a polynomial time approach to solve 3-SAT and 3-DIM-Matching instances. Probability is high that there is some flaw… [my goal with this is having fun exploring interesting questions with the limited tools I have at my disposal, and hopefully gain some insights and maybe give some ideas to more knowledgeable people]
http://arxiv.org/abs/1310.1971 (a bit behind the google doc version)
Update: the proposed method does not work. I’ve updated the document (google drive) with a detailed analysis.