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/).
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.
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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/