  This report defines various operations for weighted multi-tape automata
(WMTAs) and describes algorithms that have been implemented for those
operations in the WFSC toolkit. Some algorithms are new, others are known or
similar to known algorithms. The latter will be recalled to make this report
more complete and self-standing. We present a new approach to multi-tape
intersection, meaning the intersection of a number of tapes of one WMTA with
the same number of tapes of another WMTA. In our approach, multi-tape
intersection is not considered as an atomic operation but rather as a sequence
of more elementary ones, which facilitates its implementation. We show an
example of multi-tape intersection, actually transducer intersection, that can
be compiled with our approach but not with several other methods that we
analysed. To show the practical relavance of our work, we include an example of
application: the preservation of intermediate results in transduction cascades.
