An Ansatz for Computational Undecidability in RNA Automata

No prior work had resolved how biological polymers might emulate complex computational architectures. It was already known that nucleic acids possess the capacity for structural folding and enzymatic activity. That uncertainty drove the exploration of mapping these physical properties onto formal logic models. Prior research has shown that molecular systems can execute simple state transitions. However, the theoretical limits of such biological computing remain poorly defined. This gap motivated the current investigation into the logical boundaries of RNA-based machines. Researchers have long sought to bridge the divide between abstract computation and molecular biology. The present study addresses this by formalizing the relationship between enzymatic reactions and machine states.

The aim of this study is to formalize the theoretical construction of RNA polymers into functional automata. The authors seek to bridge the gap between molecular biology and formal computational theory. They investigate how enzymatic reactions can serve as the physical foundation for logical transitions. The researchers intend to demonstrate that these biological structures can reach the complexity of universal computers. A specific problem addressed is the emergence of computational undecidability within these self-referential systems. The study explores the implications of the Liar paradox for biological machine design. The authors also aim to propose a mechanism for how these systems might overcome logical limits. This work motivates a new perspective on the evolutionary potential of biological automata.

The review approach involves mapping enzymatic activities to formal computational states. Researchers categorize these systems by their memory capacity and transition rules. The study utilizes a hierarchical classification of automata, starting from finite models. The authors integrate concepts from recursive logic to analyze the behavior of these polymers. They evaluate the program-data duality within the context of molecular folding. The analysis focuses on the logical equivalence between enzymatic ligation and machine instructions. The team constructs theoretical models to demonstrate the progression toward universal computation. This methodology relies on mathematical abstractions of biological processes to define the limits of molecular logic.

The researchers demonstrate that RNA-based machines can achieve the computational power of a Turing machine through a 2-stack Pushdown Automaton. They show that enzymatic cleavage and ligation effectively replicate logical state transitions. The study finds that self-referential configurations inevitably lead to computational undecidability. This outcome is illustrated by the Liar paradox, which defines a hard limit on the system's logical consistency. The authors report that these boundaries are inherent to any sufficiently complex RNA-based automaton. They identify that expanding the evolutionary space allows for a hierarchical resolution of these undecidable states. This meta-systemic approach functions similarly to an oracle in classical logic. The findings suggest that these biological machines operate through a process analogous to extensible recursively generated logics.

The authors propose that RNA-based machines exhibit inherent logical constraints similar to the Liar paradox. This limitation suggests that certain configurations within these biological systems remain undecidable. The researchers suggest that expanding the evolutionary space of these machines allows for hierarchical resolution. This process mirrors the function of an oracle in classical computational theory. The study posits that such resolutions serve as a mechanism for generating biological novelty. These findings imply that RNA automata could provide a framework for understanding evolutionary complexity. The authors suggest that future work should focus on the experimental realization of these theoretical models. This synthesis highlights the potential for biological systems to transcend fixed logical boundaries through meta-systemic transitions.