On the transformation capability of feasible mechanisms for programmable matter

摘要

We study theoretical models of programmable matter systems, consisting of n spherical modules kept together by magnetic or electrostatic forces and able to perform two minimal mechanical operations (movements): rotate and/or slide. The goal is for an initial shape A to transform to some target shape B by a sequence of movements. Most of the paper focuses on transformability (feasibility) questions. When only rotation is available, we prove that deciding whether two given shapes can transform to each other, is in P. Under the additional restriction of maintaining global connectivity, we prove inclusion in PSPACE and explore minimum seeds that can make otherwise infeasible transformations feasible. Allowing both rotations and slidings yields universality: any two connected shapes of the same order can be transformed to each other without breaking connectivity, in O(n2) sequential and O(n) parallel time (both optimal). We finally provide a type of distributed transformation.