A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis
Discrete Mathematics
2014-09-08 v1
Abstract
Patterned self-assembly tile set synthesis (PATS) aims at finding a minimum tile set to uniquely self-assemble a given rectangular (color) pattern. For k >= 1, k-PATS is a variant of PATS that restricts input patterns to those with at most colors. A computer-assisted proof has been recently proposed for 2-PATS by Kari et al. [arXiv:1404.0967 (2014)]. In contrast, the best known manually-checkable proof is for the NP-hardness of 29-PATS by Johnsen, Kao, and Seki [ISAAC 2013, LNCS 8283, pp.~699-710]. We propose a manually-checkable proof for the NP-hardness of 11-PATS.
Keywords
Cite
@article{arxiv.1409.1619,
title = {A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis},
author = {Aleck Johnsen and Ming-Yang Kao and Shinnosuke Seki},
journal= {arXiv preprint arXiv:1409.1619},
year = {2014}
}