Verification and computation in restricted Tile Automata

Document Type

Article

Publication Date

6-2024

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.

Comments

Copyright © 2021, The Author(s), under exclusive licence to Springer Nature B.V.

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Publication Title

Natural Computing

DOI

https://doi.org/10.1007/s11047-021-09875-x

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