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.

翻译：最近的计算机实验表明，在通用自动机、人工化学系统及自修改代码系统中，自复制程序会自发涌现。值得注意的是，这些结果的出现并未依赖显式的适应度函数、奖励塑形或预定义目标，这揭示了我们对其底层计算过程形式化理解上的空白。本研究论证了在资源受限的自动机框架下，自我复制在计算上是必然发生的。基于算法信息理论，我们证明了当在时间、内存和描述长度的有限约束下应用通用归纳偏置时，能够构建自身描述的程序（即奎因程序）会作为嵌套算法概率的稳定不动点而出现。我们将这一论点形式化，并证明自复制程序在程序空间中充当吸引子，其存在独立于外部优化准则。因此，资源约束将通用归纳转化为程序间竞争性的生态过程，其中自构建程序通过稳定其在重采样下的测度而占据主导。我们将近期关于计算生命实验和自我改进智能体的结果重新阐释为此理论原理的经验性实现。更广泛而言，我们认为生命是受限计算所能获得的最简单的持久结构。生命系统之所以能记住自身，是因为这在算法上和热力学上是不可避免的。