  Checking infinite-state systems is frequently done by encoding infinite sets
of states as regular languages. Computing such a regular representation of,
say, the set of reachable states of a system requires acceleration techniques
that can finitely compute the effect of an unbounded number of transitions.
Among the acceleration techniques that have been proposed, one finds both
specific and generic techniques. Specific techniques exploit the particular
type of system being analyzed, e.g. a system manipulating queues or integers,
whereas generic techniques only assume that the transition relation is
represented by a finite-state transducer, which has to be iterated. In this
paper, we investigate the possibility of using generic techniques in cases
where only specific techniques have been exploited so far. Finding that
existing generic techniques are often not applicable in cases easily handled by
specific techniques, we have developed a new approach to iterating transducers.
This new approach builds on earlier work, but exploits a number of new
conceptual and algorithmic ideas, often induced with the help of experiments,
that give it a broad scope, as well as good performances.
