  We construct a small realization as flow of every precubical set (modeling
for example a process algebra). The realization is small in the sense that the
construction does not make use of any cofibrant replacement functor and of any
transfinite construction. In particular, if the precubical set is finite, then
the corresponding flow has a finite globular decomposition. Two applications
are given. The first one presents a realization functor from precubical sets to
globular complexes which is characterized up to a natural S-homotopy. The
second one proves that, for such flows, the underlying homotopy type is
naturally isomorphic to the homotopy type of the standard cubical complex
associated with the precubical set.
