Algorithms for weighted multi-tape automata

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.