PyPI 官网下载 | neural-semigroups-0.5.1.tar.gz

[](https://colab.research.google.com/github/inpefess/neural-semigroups/blob/master/examples/train_a_model.ipynb) [](https://badge.fury.io/py/neural-semigroups) [](https://circleci.com/gh/inpefess/neural-semigroups) [](https://neural-semigroups.readthedocs.io/en/latest/?badge=latest) [](https://codecov.io/gh/inpefess/neural-semigroups) # Neural Semigroups Here we try to model Cayley tables of semigroups using neural networks. The simplest way to get started is to [use Google Colaboratory](https://colab.research.google.com/github/inpefess/neural-semigroups/blob/master/examples/train_a_model.ipynb) More documentation can be found [here](https://neural-semigroups.readthedocs.io). ## Motivation This work was inspired by [a sudoku solver](https://github.com/Kyubyong/sudoku). A solved Sudoku puzzle is nothing more than a Cayley table of a quasigroup from 9 items with some well-known additional properties. So, one can imagine a puzzle made from a Cayley table of any other magma, e. g. a semigroup, by hiding part of its cells. There are two major differences between sudoku and puzzles based on semigroups: 1) it's easy to take a glance on a table to understand whether it is a sudoku or not. That's why it was possible to encode numbers in a table cells as colour intensities. Sudoku is a picture, and a semigroup is not. It's difficult to check a Cayley table's associativity with a naked eye; 2) sudoku puzzles are solved by humans for fun and thus catalogued. When solving a sudoku one knows for sure that there is a unique solution. On the contrary, nobody guesses values in a partially filled Cayley table of a semigroup as a form of amusement. As a result, one can create a puzzle from a full Cayley table of a semigroup but there may be many distinct solutions.