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arXiv · 1409.1619

A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis

Aleck Johnsen·Ming-Yang Kao·Shinnosuke Seki
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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 $k$ 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.

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Aleck Johnsen, Ming-Yang Kao, Shinnosuke Seki. 2014-09-04. A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis. https://arxiv.org/abs/1409.1619

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