A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis
Aleck Johnsen, Ming-Yang Kao, and Shinnosuke Seki

TL;DR
This paper presents a manually-checkable proof demonstrating that the problem of 11-color pattern self-assembly tile set synthesis (11-PATS) is NP-hard, improving upon previous proofs for higher color counts.
Contribution
The paper provides the first manually-checkable NP-hardness proof for 11-PATS, reducing the previously known NP-hardness threshold from 29 colors.
Findings
Proof of NP-hardness for 11-PATS
Reduction from known NP-hard problems
Improved bounds on pattern complexity
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.
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Taxonomy
TopicsAdvanced biosensing and bioanalysis techniques · DNA and Biological Computing · Modular Robots and Swarm Intelligence
