Circular splicing has been very recently introduced
to model a specific recombinant behaviour
of circular DNA, continuing the investigation initiated
with linear splicing. In this paper we restrict our
study to the
relationship between regular circular languages
and languages generated by finite circular splicing systems
and provide some results towards a characterization
of the intersection between these two classes.
We consider the class of languages X*, called
here star languages, which are closed under conjugacy
relation and with X being a regular language.
automata theory and combinatorial techniques on words, we
show that for a subclass of star languages
the corresponding circular languages
are (Paun) circular splicing languages.
For example, star languages belong
to this subclass when X* is a free monoid
or X is a finite set.
We also prove that
each (Paun) circular splicing language L
over a one-letter alphabet has the form
L = X+ ∪ Y, with X,Y finite sets satisfying
Cyclic and weak cyclic languages,
which will be introduced in this paper, show that this
result does not hold when we increase the size of
alphabets, even if we restrict ourselves to