In the REDUCE Suite, a topology is a shorthand form for exploring a sequence motif, possibly including gaps. It is a flexible and convenient way to test different motif patterns as users see fit in a particular application.
For example, X8 means an 8-mer, with 4^8=65,536 possible combinations of the four canonical DNA or RNA bases. As another example, the topology X3--X4 represents a 7-mer with a 2-nt gap in between. The k-mer size (number of X positions) can be greater than 8: the maximum number is 15. Check the source code for details.
Try the utility program Topo2Dictfile to see a list of sequences corresponding to a given topology. These are the base sequences tested by MotifREDUCE/MatrixREDUCE.
Hope this helps,
Xiang-Jun