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

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.