2013/06/13 by Lila Kari, Kari, Lila, Steffen Kopecki +3
Computer Science · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #cs.CC
paper · pdf · doi:10.48550/arxiv.1306.3257
arxiv created 2013/06/13 · arxiv updated 2013/06/17
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.