This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through pick-up, movement, and placement actions. The goal is to reconfigure a set of tiles into a specific shape termed an icicle. The icicle, identified as a dense, hole-free structure, is strategically chosen to function as an intermediate shape for more intricate shape formation tasks. It is designed for easy exploration by a finite state agent, enabling the identification of tiles that can be lifted without breaking connectivity. Compared to the line shape, the icicle presents distinct advantages, including a reduced diameter and the presence of multiple removable tiles. We propose an algorithm that transforms an arbitrary initially connected tile structure into an icicle in $\mathcal{O}(n^3)$ steps, matching the runtime of the line formation algorithm from prior work. Our theoretical contribution is accompanied by an extensive experimental analysis, indicating that our algorithm decreases the diameter of tile structures on average.

翻译：本文研究3D混合模型下的形状构造问题，在该模型中，具有严格受限视野范围和确定性有限自动机计算能力的单个智能体通过拾取、移动和放置操作来操控无源瓦片。目标是重新配置一组瓦片形成称为冰柱的特定形状。冰柱被定义为致密无孔结构，被策略性地选作更复杂形状构造任务的中介形态。其设计便于有限状态智能体探索，使得智能体能识别可在不破坏连通性的前提下被提举的瓦片。相较于线形结构，冰柱具有显著优势，包括更小的直径和存在多个可移除瓦片。我们提出一种算法，可将任意初始连接的瓦片结构在$\mathcal{O}(n^3)$步内转换为冰柱，与先前工作中线形构造算法的运行时间相匹配。我们的理论贡献辅以大量实验分析，表明该算法平均可降低瓦片结构的直径。