3-彩色有界图案化自组装
3-color Bounded Patterned Self-assembly
摘要：
图案化自组装瓦片集综合PATS是寻找一个最小瓦片集的问题，该最小瓦片集唯一地自组装成给定的图案。Czeizler和Popa证明了PATS问题的NP完全性，Seki证明了PATS问题对于60种颜色的图案已经是NP完全的。在寻找最小数量的颜色，使PATS保持NP-完全，我们引入多个绑定PATS（mbPATS），我们允许边界的瓷砖类型的每种颜色的数量。我们发现，mbPATS是NP-完全的模式，只有三种颜色，作为这个结果的副产品，我们还获得了一个新的证明的NP-完全的PATS这是比以前的证明更简洁。
英文摘要：
Patterned self-assembly tile set synthesis PATS is the problem of finding a minimal tile set which uniquely self-assembles into a given pattern. Czeizler and Popa proved the NP-completeness of PATS and Seki showed that the PATS problem is already NP-complete for patterns with 60 colors. In search for the minimal number of colors such that PATS remains NP-complete, we introduce multiple bound PATS (mbPATS) where we allow bounds for the numbers of tile types of each color. We show that mbPATS is NP-complete for patterns with just three colors and, as a byproduct of this result, we also obtain a novel proof for the NP-completeness of PATS which is more concise than the previous proofs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
