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：可编程物质的各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源，因此需要一种本地化且分布式的能量供给策略。本研究针对可编程物质的经典阿米巴机器人模型，提出了一种通用能量分配框架。该框架能够将能量无关的算法转化为行为等价且运行时开销为$\mathcal{O}(n^2)$轮的能量受限算法——即使在不公平对手下仍成立——前提是原始算法满足特定约定。我们进一步证明现有用于领导者选举（ICDCN 2023）和形态生成（Distributed Computing, 2023）的阿米巴机器人算法与该框架兼容，并通过仿真展示其能量受限版本，说明其他不公平算法如何能相对轻松地推广至能量受限场景。最后，我们证明该能量分配框架可与阿米巴机器人算法的并发控制框架（Distributed Computing, 2023）组合使用，使算法设计者能够聚焦于更简单的能量无关、顺序执行场景，同时获得能量受限、异步正确性的通用适用性。