An Ansatz for undecidable computation in RNA automata
Year: 2020
Type: preprint
Abstract: In this Ansatz we consider theoretical constructions of RNA polymers into automata, a form of computational structure. The basis for transitions in our automata are plausible RNA enzymes that may perform ligation or cleavage. Limited to these operations, we construct RNA automata of increasing complexity; from the Finite Automaton (RNA-FA) to the Turing Machine equivalent 2-stack PDA (RNA-2PDA) and the universal RNA-UPDA. For each automaton we show how the enzymatic reactions match the logical operations of the RNA automaton. A critical theme of the Ansatz is the self-reference in RNA automata configurations which exploits the program-data duality but results in undecidable computation. We describe how undecidable computation is exemplified in the self-referential Liar paradox that places a boundary on a logical system, and by construction, any RNA automata. We argue that an expansion of the evolutionary space for RNA-2PDA automata can be interpreted as a hierarchical resolution of the undecidable computation by a meta-system (akin to Turing's oracle), in a continual process analogous to Turing's ordinal logics and Post's extensible recursively generated logics. On this basis, we put forward the hypothesis that the resolution of undecidable configurations in RNA automata represent a novelty generation mechanism and propose avenues for future investigation of biological automata.
Source: arXiv (Cornell University)
Authors: Adam J. Svahn, Mikhail Prokopenko
Institution: The University of Sydney
Language: English
Topic: DNA and Biological Computing
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3194458489