We develop a framework for self-induced phase changes in programmable matter in which a collection of agents with limited computational and communication capabilities can collectively perform appropriate global tasks in response to local stimuli that dynamically appear and disappear. Agents reside on graph vertices, where each stimulus is only recognized locally, and agents communicate via token passing along edges to alert other agents to transition to an "aware" state when stimuli are present and an "unaware" state when the stimuli disappear. We present an Adaptive Stimuli Algorithm that is robust to competing waves of messages as multiple stimuli change, possibly adversarially. Moreover, in addition to handling arbitrary stimulus dynamics, the algorithm can handle agents reconfiguring the connections (edges) of the graph over time in a controlled way. As an application, we show how this Adaptive Stimuli Algorithm on reconfigurable graphs can be used to solve the foraging problem, where food sources may be discovered, removed, or shifted at arbitrary times. We would like the agents to consistently self-organize using only local interactions, such that if the food remains in position long enough, the agents transition to a gather phase, collectively forming a single large component with small perimeter around the food. Alternatively, if no food source has existed recently, the agents should self-induce a switch to a search phase in which they distribute themselves randomly throughout the lattice region to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable. Like a physical phase change, microscopic changes such as the deletion or addition of a single food source triggers these macroscopic, system-wide transitions as agents share information about the environment and respond locally to get the desired collective response.

翻译：我们提出了一种用于可编程物质中自诱导相变的理论框架，在该框架中，一群计算与通信能力有限的智能体能够对动态出现与消失的局部刺激作出响应，以集体方式执行恰当的全局任务。智能体位于图顶点上，每个刺激仅能被局部识别；智能体通过沿边传递令牌进行通信，以在刺激存在时提醒其他智能体转换至“觉察”状态，并在刺激消失时转换至“非觉察”状态。我们提出一种自适应刺激算法，该算法能够应对多个刺激可能发生的（甚至是对抗性）变化所引发的竞争性消息波。此外，除处理任意刺激动态外，该算法还能处理智能体以受控方式随时间重新配置图连接（边）的情况。作为应用，我们展示了如何利用基于可重构图的自适应刺激算法解决觅食问题——在此问题中，食物源可能在任意时刻被发现、移除或迁移。我们希望智能体仅通过局部交互实现持续自组织：若食物在固定位置停留足够长时间，智能体将过渡至聚集阶段，围绕食物集体形成一个具有小周长的大型连通组件；反之，若近期不存在食物源，智能体应自诱导切换至搜索阶段，在晶格区域内随机分布以寻找食物。与以往的觅食方法不同，该过程可无限重复。如同物理相变，单个食物源的删除或添加等微观变化会触发系统范围的宏观转变——智能体通过共享环境信息并作出局部响应，从而实现预期的集体行为。