English

The Complexity of Fixed-Height Patterned Tile Self-Assembly

Formal Languages and Automata Theory 2017-03-31 v2

Abstract

We characterize the complexity of the PATS problem for patterns of fixed height and color count in variants of the model where seed glues are either chosen or fixed and identical (so-called non-uniform and uniform variants). We prove that both variants are NP-complete for patterns of height 2 or more and admit O(n)-time algorithms for patterns of height 1. We also prove that if the height and number of colors in the pattern is fixed, the non-uniform variant admits a O(n)-time algorithm while the uniform variant remains NP-complete. The NP-completeness results use a new reduction from a constrained version of a problem on finite state transducers.

Keywords

Cite

@article{arxiv.1604.07190,
  title  = {The Complexity of Fixed-Height Patterned Tile Self-Assembly},
  author = {Shinnosuke Seki and Andrew Winslow},
  journal= {arXiv preprint arXiv:1604.07190},
  year   = {2017}
}

Comments

An abstract version appears in the proceedings of CIAA 2016

R2 v1 2026-06-22T13:39:56.489Z