  Shuffle projection is motivated by the verification of safety properties of
special parameterized systems. Basic definitions and properties, especially
related to alphabetic homomorphisms, are presented. The relation between
iterated shuffle products and shuffle projections is shown. A special class of
multi-counter automata is introduced, to formulate shuffle projection in terms
of computations of these automata represented by transductions. This
reformulation of shuffle projection leads to construction principles for pairs
of languages closed under shuffle projection. Additionally, it is shown that
under certain conditions these transductions are rational, which implies
decidability of closure against shuffle projection. Decidability of these
conditions is proven for regular languages. Finally, without additional
conditions, decidability of the question, whether a pair of regular languages
is closed under shuffle projection, is shown. In an appendix the relation
between shuffle projection and the shuffle product of two languages is
discussed. Additionally, a kind of shuffle product for computations in
S-automata is defined.
