Hierarchical Composition and
Decomposition of Permutation Groups and Transformation
A lot is going on around SgpDec. Following the upcoming GAP 4.7 a completely rewritten SgpDec will also be released.
More detailed news.
Related papers, drafts
Simple composition examples
the Skeleton of a Transformation Semigroup
Holonomy decomposition of a small automaton (cascaded automaton,
tiling picture, original automaton):