Ciliate Gene Unscrambling with Fewer Templates

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.