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Documents authored by Patitz, Matthew J.

Document
DOI: 10.4230/LIPIcs.DNA.30.3
Simulation of the Abstract Tile Assembly Model Using Crisscross Slats

Authors: Phillip Drake, Daniel Hader, and Matthew J. Patitz

Published in: LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Abstract
The abstract Tile Assembly Model (aTAM) provides an excellent foundation for the mathematical study of DNA-tile-based self-assembling systems, especially those wherein logic is embedded within the designs of the tiles so that they follow prescribed algorithms. While such algorithmic self-assembling systems are theoretically powerful, being computationally universal and capable of building complex shapes using information-theoretically optimal numbers of tiles, physical DNA-based implementations of these systems still encounter formidable error rates and undesired nucleation that hinder this theoretical potential. Slat-based self-assembly is a recent development wherein DNA forms long slats that combine together in 2 layers, rather than square tiles in a plane. In this approach, the length of the slats is key; while tiles typically only bind to 2 neighboring tiles at a time, slats may bind to dozens of other slats. This increased coordination between slats means that several mismatched slats must coincidentally meet in just the right way for errors to persist, unlike tiles where only a few are required. Consequently, while still a novel technology, large slat-based DNA constructions have been successfully implemented in the lab with resilience to many tile-based construction problems. These improved error characteristics come at a cost however, as slat-based systems are often more difficult to design and simulate than tile-based ones. Moreover, it has not been clear whether slats, with their larger sizes and different geometries, have the same theoretical capabilities as tiles. In this paper, we show that slats are capable of doing anything that tiles can, at least at scale. We demonstrate that any aTAM system may be converted to and simulated by an effectively equivalent system of slats. Furthermore, we show that these simulating slat systems can be made more efficiently, using shorter slats and a smaller scale factor, if the simulated tile system avoids certain uncommon growth patterns. Specifically, we consider 5 classes of aTAM systems with increasing complexity, from zig-zag systems which grow in a rigid pattern to the full class of all aTAM systems, and show how they may be converted to equivalent slat systems. We show that the simplest class may be simulated by slats at only a 2c × 2c scale, where c is the freely chosen coordination number of the slats, and further show that the full class of aTAM systems can be simulated at only a 5c × 5c scale. These results prove that slats have the full theoretical power of aTAM tiles while also providing constructions that are compact enough for potential DNA-based implementations of slat systems that are both capable of powerful algorithmic self-assembly and possessing of the strong error resilience of slats.
Cite as

Phillip Drake, Daniel Hader, and Matthew J. Patitz. Simulation of the Abstract Tile Assembly Model Using Crisscross Slats. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 3:1-3:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{drake_et_al:LIPIcs.DNA.30.3,
  author =	{Drake, Phillip and Hader, Daniel and Patitz, Matthew J.},
  title =	{{Simulation of the Abstract Tile Assembly Model Using Crisscross Slats}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{3:1--3:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.3},
  URN =		{urn:nbn:de:0030-drops-209315},
  doi =		{10.4230/LIPIcs.DNA.30.3},
  annote =	{Keywords: DNA origami, tile-assembly, self-assembly, aTAM, kinetic modeling, computational modeling}
}
Document
DOI: 10.4230/DagRep.13.2.183
Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091)

Authors: Aaron Becker, Sándor Fekete, Irina Kostitsyna, Matthew J. Patitz, Damien Woods, and Ioannis Chatzigiannakis

Published in: Dagstuhl Reports, Volume 13, Issue 2 (2023)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23091, "Algorithmic Foundations of Programmable Matter", a new and emerging field that combines theoretical work on algorithms with a wide spectrum of practical applications that reach all the way from small-scale embedded systems to cyber-physical structures at nano-scale. The aim of this seminar was to bring together researchers from computational geometry, distributed computing, DNA computing, and swarm robotics who have worked on programmable matter to inform one another about the newest developments in each area and to discuss future models, approaches, and directions for new research. Similar to the first two Dagstuhl Seminars on programmable matter (16271 and 18331), we did focus on some basic problems, but also considered new problems that were now within reach to be studied.
Cite as

Aaron Becker, Sándor Fekete, Irina Kostitsyna, Matthew J. Patitz, Damien Woods, and Ioannis Chatzigiannakis. Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091). In Dagstuhl Reports, Volume 13, Issue 2, pp. 183-198, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{becker_et_al:DagRep.13.2.183,
  author =	{Becker, Aaron and Fekete, S\'{a}ndor and Kostitsyna, Irina and Patitz, Matthew J. and Woods, Damien and Chatzigiannakis, Ioannis},
  title =	{{Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091)}},
  pages =	{183--198},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{2},
  editor =	{Becker, Aaron and Fekete, S\'{a}ndor and Kostitsyna, Irina and Patitz, Matthew J. and Woods, Damien and Chatzigiannakis, Ioannis},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.2.183},
  URN =		{urn:nbn:de:0030-drops-191848},
  doi =		{10.4230/DagRep.13.2.183},
  annote =	{Keywords: computational geometry, distributed algorithms, DNA computing, programmable matter, swarm robotics}
}
Document
DOI: 10.4230/LIPIcs.DNA.29.7
Accelerating Self-Assembly of Crisscross Slat Systems

Authors: David Doty, Hunter Fleming, Daniel Hader, Matthew J. Patitz, and Lukas A. Vaughan

Published in: LIPIcs, Volume 276, 29th International Conference on DNA Computing and Molecular Programming (DNA 29) (2023)

Abstract
We present an abstract model of self-assembly of systems composed of "crisscross slats", which have been experimentally implemented as a single-stranded piece of DNA [Minev et al., 2021] or as a complete DNA origami structure [Wintersinger et al., 2022]. We then introduce a more physically realistic "kinetic" model and show how important constants in the model were derived and tuned, and compare simulation-based results to experimental results [Minev et al., 2021; Wintersinger et al., 2022]. Using these models, we show how we can apply optimizations to designs of slat systems in order to lower the numbers of unique slat types required to build target structures. In general, we apply two types of techniques to achieve greatly reduced numbers of slat types. Similar to the experimental work implementing DNA origami-based slats, in our designs the slats oriented in horizontal and vertical directions are each restricted to their own plane and sets of them overlap each other in square regions which we refer to as macrotiles. Our first technique extends their previous work of reusing slat types within macrotiles and requires analyses of binding domain patterns to determine the potential for errors consisting of incorrect slat types attaching at undesired translations and reflections. The second technique leverages the power of algorithmic self-assembly to efficiently reuse entire macrotiles which self-assemble in patterns following designed algorithms that dictate the dimensions and patterns of growth. Using these designs, we demonstrate that in kinetic simulations the systems with reduced numbers of slat types self-assemble more quickly than those with greater numbers. This provides evidence that such optimizations will also result in greater assembly speeds in experimental systems. Furthermore, the reduced numbers of slat types required have the potential to vastly reduce the cost and number of lab steps for crisscross assembly experiments.
Cite as

David Doty, Hunter Fleming, Daniel Hader, Matthew J. Patitz, and Lukas A. Vaughan. Accelerating Self-Assembly of Crisscross Slat Systems. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 7:1-7:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{doty_et_al:LIPIcs.DNA.29.7,
  author =	{Doty, David and Fleming, Hunter and Hader, Daniel and Patitz, Matthew J. and Vaughan, Lukas A.},
  title =	{{Accelerating Self-Assembly of Crisscross Slat Systems}},
  booktitle =	{29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
  pages =	{7:1--7:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-297-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{276},
  editor =	{Chen, Ho-Lin and Evans, Constantine G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.29.7},
  URN =		{urn:nbn:de:0030-drops-187908},
  doi =		{10.4230/LIPIcs.DNA.29.7},
  annote =	{Keywords: DNA origami, self-assembly, kinetic modeling, computational modeling}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.71
The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly

Authors: Daniel Hader and Matthew J. Patitz

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Algorithmic self-assembly occurs when components in a disorganized collection autonomously combine to form structures and, by their design and the dynamics of the system, are forced to intrinsically follow the execution of algorithms. Motivated by applications in DNA-nanotechnology, theoretical investigations in algorithmic tile-based self-assembly have blossomed into a mature theory with research strongly leveraging tools from computability theory, complexity theory, information theory, and graph theory to develop a wide range of models and to show that many are computationally universal, while also exposing a wide variety of powers and limitations of each. In addition to computational universality, the abstract Tile-Assembly Model (aTAM) was shown to be intrinsically universal (FOCS 2012), a strong notion of completeness where a single tile set is capable of simulating the full dynamics of all systems within the model; however, this result fundamentally required non-deterministic tile attachments. This was later confirmed necessary when it was shown that the class of directed aTAM systems, those in which all possible sequences of tile attachments eventually result in the same terminal assembly, is not intrinsically universal (FOCS 2016). Furthermore, it was shown that the non-cooperative aTAM, where tiles only need to match on 1 side to bind rather than 2 or more, is not intrinsically universal (SODA 2014) nor computationally universal (STOC 2017). Building on these results to further investigate the impacts of other dynamics, Hader et al. examined several tile-assembly models which varied across (1) the numbers of dimensions used, (2) restrictions imposed on the diffusion of tiles through space, and (3) whether each system is directed, and determined which models exhibited intrinsic universality (SODA 2020). Such results have shed much light on the roles of various aspects of the dynamics of tile-assembly and their effects on the universality of each model. In this paper we extend that previous work to provide direct comparisons of the various models against each other by considering intrinsic simulations between models. Our results show that in some cases, one model is strictly more powerful than another, and in others, pairs of models have mutually exclusive capabilities. This direct comparison of models helps expose the impacts of these three important aspects of self-assembling systems, and further helps to define a hierarchy of tile-assembly models analogous to the hierarchies studied in traditional models of computation.
Cite as

Daniel Hader and Matthew J. Patitz. The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hader_et_al:LIPIcs.ICALP.2023.71,
  author =	{Hader, Daniel and Patitz, Matthew J.},
  title =	{{The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{71:1--71:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.71},
  URN =		{urn:nbn:de:0030-drops-181238},
  doi =		{10.4230/LIPIcs.ICALP.2023.71},
  annote =	{Keywords: Tile-Assembly, Tiles, aTAM, Intrinsic Simulation, Simulation}
}
Document
Extended Abstract
DOI: 10.4230/LIPIcs.DNA.28.2
Universal Shape Replication via Self-Assembly with Signal-Passing Tiles (Extended Abstract)

Authors: Andrew Alseth, Daniel Hader, and Matthew J. Patitz

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract
In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding actions of other glues via "signals". In fact, we prove our positive results in a version of the model in which it is slightly more difficult to work (where tiles are allowed to rotate) but show that they also hold in the standard STAM. Specifically, the problem we investigate is "shape replication" wherein, given a set of input assemblies of arbitrary shape, a system must construct an arbitrary number of assemblies with the same shapes and, with the exception of size-bounded junk assemblies that result from the process, no others. We provide the first fully universal shape replication result, namely a single tile set capable of performing shape replication on arbitrary sets of any 3-dimensional shapes without requiring any scaling or pre-encoded information in the input assemblies. Our result requires the input assemblies to be composed of signal-passing tiles whose glues can be deactivated to allow deconstruction of those assemblies, which we also prove is necessary by showing that there are shapes whose geometry cannot be replicated without deconstruction. Additionally, we modularize our construction to create systems capable of creating binary encodings of arbitrary shapes, and building arbitrary shapes from their encodings. Because the STAM is capable of universal computation, this then allows for arbitrary programs to be run within an STAM system, using the shape encodings as input, so that any computable transformation can be performed on the shapes.
Cite as

Andrew Alseth, Daniel Hader, and Matthew J. Patitz. Universal Shape Replication via Self-Assembly with Signal-Passing Tiles (Extended Abstract). In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 2:1-2:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alseth_et_al:LIPIcs.DNA.28.2,
  author =	{Alseth, Andrew and Hader, Daniel and Patitz, Matthew J.},
  title =	{{Universal Shape Replication via Self-Assembly with Signal-Passing Tiles}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{2:1--2:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.2},
  URN =		{urn:nbn:de:0030-drops-167876},
  doi =		{10.4230/LIPIcs.DNA.28.2},
  annote =	{Keywords: Algorithmic self-assembly, Tile Assembly Model, shape replication}
}
Document
DOI: 10.4230/LIPIcs.DNA.27.3
Self-Replication via Tile Self-Assembly (Extended Abstract)

Authors: Andrew Alseth, Daniel Hader, and Matthew J. Patitz

Published in: LIPIcs, Volume 205, 27th International Conference on DNA Computing and Molecular Programming (DNA 27) (2021)

Abstract
In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues. These modifications consist of an extension to 3D, the ability of tiles to form "flexible" bonds that allow bound tiles to rotate relative to each other, and allowing tiles of multiple shapes within the same system. We call this new model the STAM*, and we present a series of constructions within it that are capable of self-replicating behavior. Namely, the input seed assemblies to our STAM* systems can encode either "genomes" specifying the instructions for building a target shape, or can be copies of the target shape with instructions built in. A universal tile set exists for any target shape (at scale factor 2), and from a genome assembly creates infinite copies of the genome as well as the target shape. An input target structure, on the other hand, can be "deconstructed" by the universal tile set to form a genome encoding it, which will then replicate and also initiate the growth of copies of assemblies of the target shape. Since the lengths of the genomes for these constructions are proportional to the number of points in the target shape, we also present a replicator which utilizes hierarchical self-assembly to greatly reduce the size of the genomes required. The main goals of this work are to examine minimal requirements of self-assembling systems capable of self-replicating behavior, with the aim of better understanding self-replication in nature as well as understanding the complexity of mimicking it.
Cite as

Andrew Alseth, Daniel Hader, and Matthew J. Patitz. Self-Replication via Tile Self-Assembly (Extended Abstract). In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{alseth_et_al:LIPIcs.DNA.27.3,
  author =	{Alseth, Andrew and Hader, Daniel and Patitz, Matthew J.},
  title =	{{Self-Replication via Tile Self-Assembly (Extended Abstract)}},
  booktitle =	{27th International Conference on DNA Computing and Molecular Programming (DNA 27)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-205-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{205},
  editor =	{Lakin, Matthew R. and \v{S}ulc, Petr},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.27.3},
  URN =		{urn:nbn:de:0030-drops-146707},
  doi =		{10.4230/LIPIcs.DNA.27.3},
  annote =	{Keywords: Algorithmic self-assembly, tile assembly model, self-replication}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.DNA.2020
LIPIcs, Volume 174, DNA 26, Complete Volume

Authors: Cody Geary and Matthew J. Patitz

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

Abstract
LIPIcs, Volume 174, DNA 26, Complete Volume
Cite as

26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 1-230, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{geary_et_al:LIPIcs.DNA.2020,
  title =	{{LIPIcs, Volume 174, DNA 26, Complete Volume}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{1--230},
  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},
  URN =		{urn:nbn:de:0030-drops-129529},
  doi =		{10.4230/LIPIcs.DNA.2020},
  annote =	{Keywords: LIPIcs, Volume 174, DNA 26, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.DNA.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Cody Geary and Matthew J. Patitz

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{geary_et_al:LIPIcs.DNA.2020.0,
  author =	{Geary, Cody and Patitz, Matthew J.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{0:i--0:xiv},
  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.2020.0},
  URN =		{urn:nbn:de:0030-drops-129533},
  doi =		{10.4230/LIPIcs.DNA.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/DagRep.8.8.48
Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 18331)

Authors: Spring Berman, Sándor P. Fekete, Matthew J. Patitz, and Christian Scheideler

Published in: Dagstuhl Reports, Volume 8, Issue 8 (2019)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 18331,"Algorithmic Foundations of Programmable Matter", a new and emerging field that combines theoretical work on algorithms with a wide spectrum of practical applications that reach all the way from small-scale embedded systems to cyber-physical structures at nano-scale. The aim of this seminar was to bring together researchers from computational geometry, distributed computing, DNA computing, and swarm robotics who have worked on programmable matter to inform one another about the newest developments in each area and to discuss future models, approaches, and directions for new research. Similar to the first Dagstuhl seminar on programmable matter (16271), we did focus on some basic problems, but also considered new problems that were now within reach to be studied. During this seminar, we were able to achieve a previously unmatched level of intensity of collaboration, in part due to using a new electronic and interactive web-based platform. This has also allowed for continued research among the attendees based on the work begun during the seminar.
Cite as

Spring Berman, Sándor P. Fekete, Matthew J. Patitz, and Christian Scheideler. Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 18331). In Dagstuhl Reports, Volume 8, Issue 8, pp. 48-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{berman_et_al:DagRep.8.8.48,
  author =	{Berman, Spring and Fekete, S\'{a}ndor P. and Patitz, Matthew J. and Scheideler, Christian},
  title =	{{ Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 18331)}},
  pages =	{48--66},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{8},
  number =	{8},
  editor =	{Berman, Spring and Fekete, S\'{a}ndor P. and Patitz, Matthew J. and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.8.8.48},
  URN =		{urn:nbn:de:0030-drops-102352},
  doi =		{10.4230/DagRep.8.8.48},
  annote =	{Keywords: computational geometry, distributed algorithms, DNA computing, programmable matter, swarm robotics}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.172
Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM

Authors: Sarah Cannon, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Matthew J. Patitz, Robert T. Schweller, Scott M Summers, and Andrew Winslow

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
We study the difference between the standard seeded model (aTAM) of tile self-assembly, and the "seedless" two-handed model of tile self-assembly (2HAM). Most of our results suggest that the two-handed model is more powerful. In particular, we show how to simulate any seeded system with a two-handed system that is essentially just a constant factor larger. We exhibit finite shapes with a busy-beaver separation in the number of distinct tiles required by seeded versus two-handed, and exhibit an infinite shape that can be constructed two-handed but not seeded. Finally, we show that verifying whether a given system uniquely assembles a desired supertile is co-NP-complete in the two-handed model, while it was known to be polynomially solvable in the seeded model.
Cite as

Sarah Cannon, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Matthew J. Patitz, Robert T. Schweller, Scott M Summers, and Andrew Winslow. Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 172-184, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{cannon_et_al:LIPIcs.STACS.2013.172,
  author =	{Cannon, Sarah and Demaine, Erik D. and Demaine, Martin L. and Eisenstat, Sarah and Patitz, Matthew J. and Schweller, Robert T. and Summers, Scott M and Winslow, Andrew},
  title =	{{Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{172--184},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.172},
  URN =		{urn:nbn:de:0030-drops-39321},
  doi =		{10.4230/LIPIcs.STACS.2013.172},
  annote =	{Keywords: abstract tile assembly model, hierarchical tile assembly model, two-handed tile assembly model, algorithmic self-assembly, DNA computing, biocomputing}
}
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Extended Abstract
DOI: 10.4230/LIPIcs.STACS.2011.201
Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (Extended Abstract)

Authors: Erik D. Demaine, Matthew J. Patitz, Robert T. Schweller, and Scott M. Summers

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
We consider a model of algorithmic self-assembly of geometric shapes out of square Wang tiles studied in SODA 2010, in which there are two types of tiles (e.g., constructed out of DNA and RNA material) and one operation that destroys all tiles of a particular type (e.g., an RNAse enzyme destroys all RNA tiles). We show that a single use of this destruction operation enables much more efficient construction of arbitrary shapes. In particular, an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile type (related to the shape's Kolmogorov complexity), after scaling the shape by only a logarithmic factor. By contrast, without the destruction operation, the best such result has a scale factor at least linear in the size of the shape and is connected only by a spanning tree of the scaled tiles. We also characterize a large collection of shapes that can be constructed efficiently without any scaling.
Cite as

Erik D. Demaine, Matthew J. Patitz, Robert T. Schweller, and Scott M. Summers. Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (Extended Abstract). In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 201-212, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{demaine_et_al:LIPIcs.STACS.2011.201,
  author =	{Demaine, Erik D. and Patitz, Matthew J. and Schweller, Robert T. and Summers, Scott M.},
  title =	{{Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{201--212},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.201},
  URN =		{urn:nbn:de:0030-drops-30118},
  doi =		{10.4230/LIPIcs.STACS.2011.201},
  annote =	{Keywords: Biomolecular computation, RNAse enzyme self-assembly, algorithmic self-assembly, Komogorov complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2461
Intrinsic Universality in Self-Assembly

Authors: David Doty, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers, and Damien Woods

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call \emph{locally consistent}: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly. Our construction is reminiscent of the studies of \emph{intrinsic universality} of cellular automata by Ollinger and others, in the sense that our simulation of a tile system $T$ by a tile system $U$ represents each tile in an assembly produced by $T$ by a $c \times c$ block of tiles in $U$, where $c$ is a constant depending on $T$ but not on the size of the assembly $T$ produces (which may in fact be infinite). Also, our construction improves on earlier simulations of tile assembly systems by other tile assembly systems (in particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we simulate the actual process of self-assembly, not just the end result, as in Soloveichik and Winfree's construction, and we do not discriminate against infinite structures. Both previous results simulate only temperature 1 systems, whereas our construction simulates tile assembly systems operating at temperature 2.
Cite as

David Doty, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers, and Damien Woods. Intrinsic Universality in Self-Assembly. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 275-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{doty_et_al:LIPIcs.STACS.2010.2461,
  author =	{Doty, David and Lutz, Jack H. and Patitz, Matthew J. and Summers, Scott M. and Woods, Damien},
  title =	{{Intrinsic Universality in Self-Assembly}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{275--286},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2461},
  URN =		{urn:nbn:de:0030-drops-24619},
  doi =		{10.4230/LIPIcs.STACS.2010.2461},
  annote =	{Keywords: Biological computing, Molecular computation, intrinsic universality, self-assembly}
}
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