Individual modules of programmable matter participate in their system's collective behavior by expending energy to perform actions. However, not all modules may have access to the external energy source powering the system, necessitating a local and distributed strategy for supplying energy to modules. In this work, we present a general energy distribution framework for the canonical amoebot model of programmable matter that transforms energy-agnostic algorithms into energy-constrained ones with equivalent behavior and an $\mathcal{O}(n^2)$-round runtime overhead -- even under an unfair adversary -- provided the original algorithms satisfy certain conventions. We then prove that existing amoebot algorithms for leader election (ICDCN 2023) and shape formation (Distributed Computing, 2023) are compatible with this framework and show simulations of their energy-constrained counterparts, demonstrating how other unfair algorithms can be generalized to the energy-constrained setting with relatively little effort. Finally, we show that our energy distribution framework can be composed with the concurrency control framework for amoebot algorithms (Distributed Computing, 2023), allowing algorithm designers to focus on the simpler energy-agnostic, sequential setting but gain the general applicability of energy-constrained, asynchronous correctness.

翻译：可编程物质的单个模块通过消耗能量执行动作来参与系统的集体行为。然而，并非所有模块都能接入为系统供电的外部能量源，这需要为模块供能制定局部且分布式的策略。本文针对可编程物质的典型阿米巴虫模型，提出了一种通用能量分布框架。该框架能够将不涉及能量约束的算法转化为能量受限且行为等价的版本，即使在不公平对抗条件下，若原始算法满足特定约定，其运行时开销仅为$\mathcal{O}(n^2)$轮。我们进一步证明，现有用于领导者选举（ICDCN 2023）和形状形成（Distributed Computing, 2023）的阿米巴虫算法与该框架兼容，并通过仿真展示其能量受限对应版本，从而说明其他不公平算法如何以相对较小的代价推广至能量受限场景。最后，我们证明该能量分布框架可与阿米巴虫算法的并发控制框架（Distributed Computing, 2023）组合，使得算法设计师能够专注于更简单的无能量约束的顺序场景，同时获得能量受限异步正确性的广泛适用性。