3 Search Results for "Jonoska, Nataša"

Document
DOI: 10.4230/LIPIcs.SAND.2025.14
Fractals in Seeded Tile Automata

Authors: Asher Haun, Ryan Knobel, Adrian Salinas, Ramiro Santos, Robert Schweller, and Tim Wylie

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
This work fully characterizes fractal generation in the seeded Tile Automata model (seeded TA), a model similar to the abstract Tile Assembly model (aTAM) with the added ability for adjacent tiles to change states. Under these assumptions, we first show that all discrete self-similar fractals (DSSFs) with feasible generators are strictly buildable at scale 1 and temperature 1 in seeded TA. We then show that these results imply the existence of a single seeded TA system Γ that can strictly build any DSSF infinitely at scale 1 and temperature 1.
Cite as

Asher Haun, Ryan Knobel, Adrian Salinas, Ramiro Santos, Robert Schweller, and Tim Wylie. Fractals in Seeded Tile Automata. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haun_et_al:LIPIcs.SAND.2025.14,
  author =	{Haun, Asher and Knobel, Ryan and Salinas, Adrian and Santos, Ramiro and Schweller, Robert and Wylie, Tim},
  title =	{{Fractals in Seeded Tile Automata}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.14},
  URN =		{urn:nbn:de:0030-drops-230677},
  doi =		{10.4230/LIPIcs.SAND.2025.14},
  annote =	{Keywords: self-assembly, tile automata, fractals}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.48
Subshifts Defined by Nondeterministic and Alternating Plane-Walking Automata

Authors: Benjamin Hellouin de Menibus and Pacôme Perrotin

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Plane-walking automata were introduced by Salo & Törma to recognise languages of two-dimensional infinite words (subshifts), the counterpart of 4-way finite automata for two-dimensional finite words. We extend the model to allow for nondeterminism and alternation of quantifiers. We prove that the recognised subshifts form a strict subclass of sofic subshifts, and that the classes corresponding to existential and universal nondeterminism are incomparable and both larger that the deterministic class. We define a hierarchy of subshifts recognised by plane-walking automata with alternating quantifiers, which we conjecture to be strict.
Cite as

Benjamin Hellouin de Menibus and Pacôme Perrotin. Subshifts Defined by Nondeterministic and Alternating Plane-Walking Automata. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hellouindemenibus_et_al:LIPIcs.STACS.2025.48,
  author =	{Hellouin de Menibus, Benjamin and Perrotin, Pac\^{o}me},
  title =	{{Subshifts Defined by Nondeterministic and Alternating Plane-Walking Automata}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{48:1--48:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.48},
  URN =		{urn:nbn:de:0030-drops-228540},
  doi =		{10.4230/LIPIcs.STACS.2025.48},
  annote =	{Keywords: Formal languages, Finite automata, Subshifts, Symbolic dynamics, Tilings}
}
Document
DOI: 10.4230/LIPIcs.DNA.2020.1
The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes

Authors: Abdulmelik Mohammed, Nataša Jonoska, and Masahico Saito

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract
The routing of a DNA-origami scaffold strand is often modelled as an Eulerian circuit of an Eulerian graph in combinatorial models of DNA origami design. The knot type of the scaffold strand dictates the feasibility of an Eulerian circuit to be used as the scaffold route in the design. Motivated by the topology of scaffold routings in 3D DNA origami, we investigate the knottedness of Eulerian circuits on surface-embedded graphs. We show that certain graph embeddings, checkerboard colorable, always admit unknotted Eulerian circuits. On the other hand, we prove that if a graph admits an embedding in a torus that is not checkerboard colorable, then it can be re-embedded so that all its non-intersecting Eulerian circuits are knotted. For surfaces of genus greater than one, we present an infinite family of checkerboard-colorable graph embeddings where there exist knotted Eulerian circuits.
Cite as

Abdulmelik Mohammed, Nataša Jonoska, and Masahico Saito. The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mohammed_et_al:LIPIcs.DNA.2020.1,
  author =	{Mohammed, Abdulmelik and Jonoska, Nata\v{s}a and Saito, Masahico},
  title =	{{The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{1:1--1:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.1},
  URN =		{urn:nbn:de:0030-drops-129540},
  doi =		{10.4230/LIPIcs.DNA.2020.1},
  annote =	{Keywords: DNA origami, Scaffold routing, Graphs, Surfaces, Knots, Eulerian circuits}
}
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