  Geometric folding processes are ubiquitous in natural systems ranging from
protein biochemistry to patterns of insect wings and leaves. In a previous
study, a folding operation between strings of formal languages was introduced
as a model of such processes. The operation was then used to define a folding
system (F-system) as a construct consisting of a core language, containing the
strings to be folded, and a folding procedure language, which defines how the
folding is done. This paper reviews main definitions associated with F-systems
and next it determines necessary conditions for a language to belong to classes
generated by such systems. The conditions are stated in the form of pumping
lemmas and four classes are considered, in which the core and folding procedure
languages are both regular, one of them is regular and the other context-free,
or both are context-free. Full demonstrations of the lemmas are provided, and
the analysis is illustrated with examples.
