  A weighted finite-state machine with n tapes (n-WFSM) defines a rational
relation on n strings. It is a generalization of weighted acceptors (one tape)
and transducers (two tapes).
  After recalling some basic definitions about n-ary weighted rational
relations and n-WFSMs, we summarize some central operations on these relations
and machines, such as join and auto-intersection. Unfortunately, due to Post's
Correspondence Problem, a fully general join or auto-intersection algorithm
cannot exist. We recall a restricted algorithm for a class of n-WFSMs.
  Through a series of practical applications, we finally investigate the
augmented descriptive power of n-WFSMs and their join, compared to classical
transducers and their composition. Some applications are not feasible with the
latter. The series includes: the morphological analysis of Semitic languages,
the preservation of intermediate results in transducer cascades, the induction
of morphological rules from corpora, the alignment of lexicon entries, the
automatic extraction of acronyms and their meaning from corpora, and the search
for cognates in a bilingual lexicon.
  All described operations and applications have been implemented with Xerox's
WFSC tool.
