  Language theory, symbolic dynamics, modelisation of viral insertion into the
genetic code of a host cell motivate the introduction of new types of
bialgebras whose coalgebra parts are not necessarily coassociative. One of the
aim of this article is to study what type of (associative) algebras (and thus
binary quadratic and non-symmetric operads) appear when such or such
coalgebraic structures are used to decribe for instance combinatorial objects
such as weighted directed graphs, trees, substitutions and so forth.
