Sgpdec

GAP package for Hierarchical Composition and Decomposition of Permutation Groups and Transformation Semigroups

View the Project on GitHub gap-packages/sgpdec

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SgpDec: Hierarchical Composition and Decomposition of Permutation Groups and Transformation Semigroups

What is it good for?

Decomposing transformation semigroups and permutation groups into cascade (sub-wreath) products of simpler components. In other words, understanding the structure of finite computations.

In the long run, it is meant to be game changing in artificial intelligence, systems biology, physics, or in any field where models with discrete states make sense.

For a lightweight popular science style reading on computational semigroup theory check the computational semigroup theory blog (https://compsemi.wordpress.com/).

How to use it?

You need the latest version of the GAP computer algebra system (https://github.com/gap-system/gap).

To get some idea what SgpDec is capable of, check this paper: SgpDec: Cascade (De)Compositions of Finite Transformation Semigroups and Permutation Groups (http://link.springer.com/chapter/10.1007/978-3-662-44199-2_13). For further details the documentation should be helpful.

The preprint Computational Holonomy Decomposition of Transformation Semigroups http://arxiv.org/abs/1508.06345 contains a constructive proof of the holonomy decomposition that is in close correspondence to the implementation.

Where to complain when something goes wrong?

Please report any problem or request features by creating on issue on the project page here.

Who are you?

Attila Egri-Nagy www.egri-nagy.hu @EgriNagy

James D. Mitchell http://www-groups.mcs.st-andrews.ac.uk/~jamesm/ @jdmjdmjdmjdm

Chrystopher L. Nehaniv http://homepages.herts.ac.uk/~comqcln/