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Synchronous Versus Asynchronous Tile-Based Self-Assembly

Authors Florent Becker , Phillip Drake , Matthew J. Patitz , Trent A. Rogers

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Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • self-assembly
  • noncooperative self-assembly
  • models of computation
  • tile assembly systems

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Abstract

In this paper we study the relationship between mathematical models of tile-based self-assembly which differ in terms of the synchronicity of tile additions. In the standard abstract Tile Assembly Model (aTAM), each step of assembly consists of a single tile being added to an assembly. At any given time, each location on the perimeter of an assembly to which a tile can legally bind is called a frontier location, and for each step of assembly one frontier location is randomly selected and a tile is added. In the Synchronous Tile Assembly Model (syncTAM), at each step of assembly every frontier location simultaneously receives a tile.
Our results show that while directed, non-cooperative syncTAM systems are capable of universal computation (while directed, non-cooperative aTAM systems are known not to be), and they are capable of building shapes that can't be built within the aTAM, the non-cooperative aTAM is also capable of building shapes that can't be built within the syncTAM even cooperatively. We show a variety of results that demonstrate the similarities and differences between these two models.

Cite As Get BibTex

Florent Becker, Phillip Drake, Matthew J. Patitz, and Trent A. Rogers. Synchronous Versus Asynchronous Tile-Based Self-Assembly. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DNA.31.9

Author Details

Florent Becker
  • Laboratoire d’Informatique Fondamentale d’Orléans (UR4022), Université d’Orléans, France
Phillip Drake
  • University of Arkansas, Fayetteville, AR, USA
Matthew J. Patitz
  • University of Arkansas, Fayetteville, AR, USA
Trent A. Rogers
  • University of Arkansas, Fayetteville, AR, USA

Funding

  • Becker, Florent: Research made at a public, state-funded university, thanks to the guarantee of full academic freedom and perennial research funding.
  • Drake, Phillip: This author’s work was supported in part by NSF grant 2329908.
  • Patitz, Matthew J.: This author’s work was supported in part by NSF grant 2329908.

Supplementary Materials

References

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