Proving the Turing Universality of Oritatami Co-Transcriptional Folding (Full Text)
Cody Geary, Pierre-\'Etienne Meunier, Nicolas Schabanel, Shinnosuke, Seki

TL;DR
This paper demonstrates that the oritatami model for molecular co-transcriptional folding can simulate universal computation, providing a framework with reusable tools and proof certificates for complex system behavior.
Contribution
It introduces a generic toolbox and a multi-level programming framework that embed universal computation into the oritatami folding process, enabling formal correctness proofs.
Findings
Proved the universality of the oritatami folding model.
Developed reusable low-level tools for encoding functions.
Created a proof certification method with human-readable certificates.
Abstract
We study the oritatami model for molecular co-transcriptional folding. In oritatami systems, the transcript (the "molecule") folds as it is synthesized (transcribed), according to a local energy optimisation process, which is similar to how actual biomolecules such as RNA fold into complex shapes and functions as they are transcribed. We prove that there is an oritatami system embedding universal computation in the folding process itself. Our result relies on the development of a generic toolbox, which is easily reusable for future work to design complex functions in oritatami systems. We develop "low-level" tools that allow to easily spread apart the encoding of different "functions" in the transcript, even if they are required to be applied at the same geometrical location in the folding. We build upon these low-level tools, a programming framework with increasing levels of…
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