The computational inevitability of life: self-replication under resource-bounded nested algorithmic probability

TL;DR

This paper demonstrates that under resource constraints, self-replicating programs naturally emerge as stable fixed points in program space, explaining the spontaneous appearance of life-like systems without explicit objectives.

Contribution

It formalizes the computational inevitability of self-replication using algorithmic information theory under resource bounds, linking life to constrained universal induction.

Findings

Self-replicating programs act as attractors in program space.

Resource bounds lead to stable self-constructing programs.

Empirical results align with the theoretical model.

Abstract

Recent computational experiments have demonstrated the spontaneous emergence of self-replicating programs across universal automata, artificial chemistries, and self-modifying code systems. Remarkably, these results arise without explicit fitness functions, reward shaping, or predefined objectives, indicating a gap in our formal understanding of the underlying computational process. In this work, we argue that self-replication is computationally inevitable under resource-bounded automata. Building on algorithmic information theory, we show that when universal inductive bias is applied under finite constraints of time, memory, and description length, programs that construct descriptions of themselves, i.e., quines, emerge as stable fixed points of nested algorithmic probability. We formalize this argument and demonstrate that self-replicating programs act as attractors in program space, independent of external optimization criteria. Thus, resource bounds transform universal induction into a competitive ecological process over programs, in which self-constructing programs dominate by stabilizing their own measure under resampling. We reinterpret recent results from computational life experiments and self-improving artificial agents as empirical realizations of this theoretical principle. More broadly, we propose that life is the simplest persistent structure available to constrained computation. A living system remembers itself because doing so is algorithmically and thermodynamically unavoidable.