分层自组装中的乘积

摘要：

三个结果显示在积的层次模型的瓷砖自组装。结果表明，一个简单的贪婪多项式时间策略决定是否是一个组件A是可生产的。该算法可以优化为O（|A| log^2 |A|）时间。Cannon，Demaine，Demaine，Eisenstat，Patitz，Schweller，Summers，and Winslow证明了对于非合作的"温度1"系统的特殊情况，判定一个组件A是否是瓦片系统T的唯一可产生终端组件的问题可以在O（|A| ^2 |T| + |A| |T| ^2）时间内解决。它表明，这可以提高到O（|A| |T| log |T|）的时间。最后，它表明，如果两个组件是可生产的，如果他们可以重叠一致-即，如果它们共享的位置在每个组合中具有相同的瓦片类型--那么它们的并集也是可产生的。

英文摘要：

Three results are shown on producibility in the hierarchical model of tile self-assembly. It is shown that a simple greedy polynomial-time strategy decides whether an assembly A is producible. The algorithm can be optimized to use O(|A| log^2 |A|) time. Cannon, Demaine, Demaine, Eisenstat, Patitz, Schweller, Summers, and Winslow showed that the problem of deciding if an assembly A is the unique producible terminal assembly of a tile system T can be solved in O(|A|^2 |T| + |A| |T|^2) time for the special case of noncooperative "temperature 1" systems. It is shown that this can be improved to O(|A| |T| log |T|) time. Finally, it is shown that if two assemblies are producible, and if they can be overlapped consistently -- i.e., if the positions that they share have the same tile type in each assembly -- then their union is also producible.

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