Multi-level control mechanisms for non-structured and structured 2-dimensional self-assembling

We present a multi-level approach to control the assembling of 2-dimensional patterns. The top control level uses abstract tiles, where the borders and the bodies of the tiles are labeled by abstract symbols. Tile assembling requires the match of border labels on the common borders, leading to specific 2-dimensional patterns. Further control levels may be introduced adding new data (on borders) and relations connecting these data (on bodies). This refinement process may be repeated going from an abstract and often nondeterministic self-assembling specification to a more controlled and detailed targeted specification-the former may be more related to the infrastructure, while the latter with the functionality mapped on that infrastructure. The approach is further instantiated to work with both non structured and structured control mechanisms. The first one uses border labels to control tile assembling. It has a more pronounced self-assembling character, where tiles have little knowledge on the emerging result. The second, structured approach takes advantage on a recently introduced new class of 2-dimensional regular expressions. These expressions are based on a global knowledge of the resulted patterns and on their generation. It is a higher level control mechanism letting tiles and their composites to assemble according to the shapes described by these expressions. While the approach may be used with any kind of interpretation of the dimensions, our applications have focused on the case when one dimension represents space and the other time. In this case, the approach has produced non-structured and structured models and programming languages for open, interactive, distributed processes. We illustrate the approach with the sketch of a program for smart-car modeling.