Since predicate-augmented finite state recognizers are equivalent to
ordinary finite-state automata, the class of languages defined by
psfr is closed under the the usual regular operations such as *
union*, * concatenation*, * Kleene-closure* and *
reversal*. From a practical point of view, however, it is
interesting to note that it is trivial to generalize the
corresponding constructions for classical finite state automata (cf. for instance [13]). This means that the various
constructions can be implemented directly, without the need to expand
into ordinary finite automata first, which is impractical for large
alphabets.