A method factors an ambiguous finite state transducer (FST) into two finite state
transducers. The first FST is functional (i.e., unambiguous). The second FST retains
the ambiguity of the original FST but is fail-safe (i.e., no failing paths) when
applied to the output of the first FST. That is, the application of the second
FST to an input string never leads to a state that does not provide a transition
for the next symbol in the input. Subsequently, the first FST can be factorized
into a left-sequential FST and a right-sequential FST that jointly represent a bi-machine.