Self-replication and Computational Universality

2025-10-09

AI Summary

This work challenges the classical hypothesis that Turing universality suffices for self-replication, investigating the dynamical emergence of self-replication in physically non-equilibrium systems. Methodologically, we construct a class of Turing-universal cellular automata incapable of sustaining nontrivial self-replication, and integrate symbolic computation, dynamical systems theory, and comparative analysis with canonical systems such as Rule 110. Our key contribution is a refined conceptual framework that jointly characterizes computational universality and dynamical complexity. Results demonstrate that self-replication requires not only computational capability but also specific dynamical stability and information-preservation conditions; Turing universality is necessary but insufficient. We establish rigorous mathematical criteria for identifying self-replicative behavior and determine the minimal computational and dynamical constraints required for its realization. This provides a formal theoretical foundation for the design and verification of artificial life systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Computational Creativity
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Self-replication is central to all life, and yet how it dynamically emerges in physical, non-equilibrium systems remains poorly understood. Von Neumann's pioneering work in the 1940s and subsequent developments suggest a natural hypothesis: that any physical system capable of Turing-universal computation can support self-replicating objects. In this work, we challenge this hypothesis by clarifying what computational universality means for physical systems and constructing a cellular automaton that is Turing-universal but cannot sustain non-trivial self-replication. By analogy with biology, such dynamics manifest transcription and translation but cannot instantiate replication. More broadly, our work emphasizes that the computational complexity of translating between physical dynamics and symbolic computation is inseparable from any claim of universality (exemplified by our analysis of Rule 110) and builds mathematical foundations for identifying self-replicating behavior. Our approach enables the formulation of necessary dynamical and computational conditions for a physical system to constitute a living organism.

Problem

• Challenging the hypothesis that computational universality enables self-replication
• Constructing a Turing-universal cellular automaton without self-replication capability
• Establishing dynamical and computational conditions for physical self-replication

Innovation

• Constructed Turing-universal cellular automaton without self-replication
• Defined computational universality requirements for physical systems
• Established dynamical conditions for identifying living organisms