Solving a new NP-Complete problem that resembles image pattern recognition using deep learning

Abstract

In computer science, non-deterministic polynomialtime
 (NP) denotes the set of problems for which a
 solution might or might not be found quickly but can
 be checked quickly. We also call the set of problems
 in NP that are at least as hard as any other NP problem
 non-deterministic polynomial-time complete (NPcomplete).
 Although not known if they can be solved
 quickly, NP-complete problems can be converted
 into one another quickly. A prominent and practical
 example is the protein folding problem, which is a
 problem of determining the shape and function of
 proteins. In this paper, we discovered and provided
 a mathematical proof of a new NP-complete problem,
 that we named 3-Grid Pattern Decision Problem (3-
 GPDP). 3-GPDP is a decision problem that asks if a
 specific kind of pattern exists or not on a grid/matrix
 of numbers consisting of zeros and ones, much like
 image recognition. We hypothesized that a neural net
 would be able to solve 3-GPDP problems with high
 accuracy and low loss when trained. In support of
 our hypothesis, our experiment resulted in a neural
 net that performed with 84% accuracy and 0.14 loss
 without underfitting or overfitting. Moreover, there
 was also an increase in accuracy and decrease in
 loss with more training data. As a result, since neural
 networks are effective at solving 3-GPDP problems,
 which are NP-complete, then we can convert important
 NP-complete problems into 3-GPDP problems, solve
 the 3-GPDP problems using neural networks, and
 convert the solution back to the solution of the initial
 problem, quickly.