Ciliate Gene Unscrambling with Fewer Templates

TL;DR

This paper refines the template-guided recombination model for gene unscrambling in ciliates, enabling regular language generation with fewer templates and extending the system to achieve Turing completeness using finite components.

Contribution

It introduces a more efficient TGR model with fewer templates and extends the CTGR system with permitting contexts to attain Turing completeness with finite resources.

Findings

Generated regular languages with fewer templates.

Extended CTGR system to include permitting contexts.

Achieved Turing completeness with finite initial language and templates.

Abstract

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.