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Verification and Computation in Restricted Tile Automata

Authors David Caballero, Timothy Gomez, Robert Schweller, Tim Wylie

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Author Details

David Caballero
  • Department of Computer Science, University of Texas, Rio Grande Valley, TX, USA
Timothy Gomez
  • Department of Computer Science, University of Texas, Rio Grande Valley, TX, USA
Robert Schweller
  • Department of Computer Science, University of Texas, Rio Grande Valley, TX, USA
Tim Wylie
  • Department of Computer Science, University of Texas, Rio Grande Valley, TX, USA

Funding

This research was supported in part by National Science Foundation Grant CCF-1817602.

Cite AsGet BibTex

David Caballero, Timothy Gomez, Robert Schweller, and Tim Wylie. Verification and Computation in Restricted Tile Automata. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.DNA.2020.10

Abstract

Many models of self-assembly have been shown to be capable of performing computation. Tile Automata was recently introduced combining features of both Celluar Automata and the 2-Handed Model of self-assembly both capable of universal computation. In this work we study the complexity of Tile Automata utilizing features inherited from the two models mentioned above. We first present a construction for simulating Turing Machines that performs both covert and fuel efficient computation. We then explore the capabilities of limited Tile Automata systems such as 1-Dimensional systems (all assemblies are of height 1) and freezing Systems (tiles may not repeat states). Using these results we provide a connection between the problem of finding the largest uniquely producible assembly using n states and the busy beaver problem for non-freezing systems and provide a freezing system capable of uniquely assembling an assembly whose length is exponential in the number of states of the system. We finish by exploring the complexity of the Unique Assembly Verification problem in Tile Automata with different limitations such as freezing and systems without the power of detachment.

Subject Classification

ACM Subject Classification
  • Theory of computation → Turing machines
  • Computer systems organization → Molecular computing
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Tile Automata
  • Turing Machines
  • Unique Assembly Verification

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