  One of the theoretical models proposed for the mechanism of gene unscrambling
in some species of ciliates is the template-guided recombination (TGR) system
by Prescott, Ehrenfeucht and Rozenberg which has been generalized by Daley and
McQuillan from a formal language theory perspective. In this paper, we propose
a refinement of this model that generates regular languages using the iterated
TGR system with a finite initial language and a finite set of templates, using
fewer templates and a smaller alphabet compared to that of the Daley-McQuillan
model. To achieve Turing completeness using only finite components, i.e., a
finite initial language and a finite set of templates, we also propose an
extension of the contextual template-guided recombination system (CTGR system)
by Daley and McQuillan, by adding an extra control called permitting contexts
on the usage of templates.
