26 Search Results for "Schweller, Robert"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.14
General Computation Using Slidable Tiles with Deterministic Global Forces

Authors: Alberto Avila-Jimenez, David Barreda, Sarah-Laurie Evans, Austin Luchsinger, Aiden Massie, Robert Schweller, Evan Tomai, and Tim Wylie

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study the computational power of the Full-Tilt model of motion planning, where slidable polyominos are moved maximally around a board by way of a sequence of directional "tilts." We focus on the deterministic scenario in which the tilts constitute a repeated clockwise rotation. We show that general-purpose computation is possible within this framework by providing a direct and efficient simulation of space-bounded Turing machines in which one computational step of the machine is simulated per O(1) rotations. We further show that the initial tape of the machine can be programmed by an initial tilt-sequence preceding the rotations. This result immediately implies new PSPACE-completeness results for the well-studied problems of occupancy (deciding if a given board location can be occupied by a tile), vacancy (deciding if a location can be emptied), relocation (deciding if a tile can be moved from one location to another), and reconfiguration (can a given board configuration be reconfigured into a second given configuration) that hold even for deterministically repeating tilt cycles such as rotations. All of our PSPACE-completeness results hold even when there is only a single domino in the system beyond singleton tiles. Following, we show that these results work in the Single-Step tilt model for larger constant cycles. We then investigate computational efficiency by showing a modification to implement a two-tape Turing machine in the Full-Tilt model and Systolic Arrays in the Single-Step model. Finally, we show a cyclic implementation for tilt-efficient Threshold Circuits.
Cite as

Alberto Avila-Jimenez, David Barreda, Sarah-Laurie Evans, Austin Luchsinger, Aiden Massie, Robert Schweller, Evan Tomai, and Tim Wylie. General Computation Using Slidable Tiles with Deterministic Global Forces. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{avilajimenez_et_al:LIPIcs.ITCS.2026.14,
  author =	{Avila-Jimenez, Alberto and Barreda, David and Evans, Sarah-Laurie and Luchsinger, Austin and Massie, Aiden and Schweller, Robert and Tomai, Evan and Wylie, Tim},
  title =	{{General Computation Using Slidable Tiles with Deterministic Global Forces}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{14:1--14:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.14},
  URN =		{urn:nbn:de:0030-drops-253019},
  doi =		{10.4230/LIPIcs.ITCS.2026.14},
  annote =	{Keywords: motion planning, global control, external forces, deterministic computation, occupancy, vacancy}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.7
Polynomial Equivalence of Extended Chemical Reaction Models

Authors: Divya Bajaj, Jose-Luis Castellanos, Ryan Knobel, Austin Luchsinger, Aiden Massie, Adrian Salinas, Pablo Santos, Ramiro Santos, Robert Schweller, and Tim Wylie

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The ability to detect whether a species (or dimension) is zero in Chemical Reaction Networks (CRN), Vector Addition Systems, or Petri Nets is known to increase the power of these models - making them capable of universal computation. While this ability may appear in many forms, such as extending the models to allow transitions to be inhibited, prioritized, or synchronized, we present an extension that directly performs this zero checking. We introduce a new void genesis CRN variant with a simple design that merely increments the count of a specific species when any other species' count goes to zero. As with previous extensions, we show that the model is Turing Universal. We then analyze several other studied CRN variants and show that they are all equivalent through a polynomial simulation with the void genesis model, which does not merely follow from Turing-universality. Thus, inhibitor species, reactions that occur at different rates, being allowed to run reactions in parallel, or even being allowed to continually add more volume to the CRN, does not add additional simulation power beyond simply detecting if a species count becomes zero.
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Divya Bajaj, Jose-Luis Castellanos, Ryan Knobel, Austin Luchsinger, Aiden Massie, Adrian Salinas, Pablo Santos, Ramiro Santos, Robert Schweller, and Tim Wylie. Polynomial Equivalence of Extended Chemical Reaction Models. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bajaj_et_al:LIPIcs.ISAAC.2025.7,
  author =	{Bajaj, Divya and Castellanos, Jose-Luis and Knobel, Ryan and Luchsinger, Austin and Massie, Aiden and Salinas, Adrian and Santos, Pablo and Santos, Ramiro and Schweller, Robert and Wylie, Tim},
  title =	{{Polynomial Equivalence of Extended Chemical Reaction Models}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.7},
  URN =		{urn:nbn:de:0030-drops-249158},
  doi =		{10.4230/LIPIcs.ISAAC.2025.7},
  annote =	{Keywords: Chemical Reaction Networks, Simulations, Petri-nets, Vector Addition Systems, Bi-simulation, Turing-universality, Inhibitors}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.51
Graph Tiles (Poster Abstract)

Authors: Oswin Aichholzer, Robert Ganian, Phillip Keldenich, Maarten Löffler, Gert Meijer, Alexandra Weinberger, and Carola Wenk

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We define a graph tile to be a unit square (or more generally, a polygon) on which a piece of a graph has been drawn/embedded; in particular, it may have vertices in its interior, edges connecting those vertices, or half-edges that extend to the boundary of the tile. In a graph tiling problem, we are given as input a set of graph tiles, with multiplicities, and the output is an arrangement of those tiles forming a graph of larger area. We focus on a simple tile set: unit square tiles with a central vertex and either a half-edge or no half-edge on each side. Up to symmetry this gives us six different types. We characterize which multiplicities are compatible for sets of at most three different tiles.
Cite as

Oswin Aichholzer, Robert Ganian, Phillip Keldenich, Maarten Löffler, Gert Meijer, Alexandra Weinberger, and Carola Wenk. Graph Tiles (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 51:1-51:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.51,
  author =	{Aichholzer, Oswin and Ganian, Robert and Keldenich, Phillip and L\"{o}ffler, Maarten and Meijer, Gert and Weinberger, Alexandra and Wenk, Carola},
  title =	{{Graph Tiles}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{51:1--51:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.51},
  URN =		{urn:nbn:de:0030-drops-250371},
  doi =		{10.4230/LIPIcs.GD.2025.51},
  annote =	{Keywords: graph tiles}
}
Document
DOI: 10.4230/LIPIcs.DNA.31.1
Algorithmic Hardness of the Partition Function for Nucleic Acid Strands

Authors: Gwendal Ducloz, Ahmed Shalaby, and Damien Woods

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

Abstract
To understand and engineer biological and artificial nucleic acid systems, algorithms are employed for prediction of secondary structures at thermodynamic equilibrium. Dynamic programming algorithms are used to compute the most favoured, or Minimum Free Energy (MFE), structure, and the Partition Function (PF) - a tool for assigning a probability to any structure. However, in some situations, such as when there are large numbers of strands, or pseudoknotted systems, NP-hardness results show that such algorithms are unlikely, but only for MFE. Curiously, algorithmic hardness results were not shown for PF, leaving two open questions on the complexity of PF for multiple strands and single strands with pseudoknots. The challenge is that while the MFE problem cares only about one, or a few structures, PF is a summation over the entire secondary structure space, giving theorists the vibe that computing PF should not only be as hard as MFE, but should be even harder. We answer both questions. First, we show that computing PF is #P-hard for systems with an unbounded number of strands, answering a question of Condon Hajiaghayi, and Thachuk [DNA27]. Second, for even a single strand, but allowing pseudoknots, we find that PF is #P-hard. Our proof relies on a novel magnification trick that leads to a tightly-woven set of reductions between five key thermodynamic problems: MFE, PF, their decision versions, and #SSEL that counts structures of a given energy. Our reductions show these five problems are fundamentally related for any energy model amenable to magnification. That general classification clarifies the mathematical landscape of nucleic acid energy models and yields several open questions.
Cite as

Gwendal Ducloz, Ahmed Shalaby, and Damien Woods. Algorithmic Hardness of the Partition Function for Nucleic Acid Strands. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ducloz_et_al:LIPIcs.DNA.31.1,
  author =	{Ducloz, Gwendal and Shalaby, Ahmed and Woods, Damien},
  title =	{{Algorithmic Hardness of the Partition Function for Nucleic Acid Strands}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{1:1--1:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.1},
  URN =		{urn:nbn:de:0030-drops-238504},
  doi =		{10.4230/LIPIcs.DNA.31.1},
  annote =	{Keywords: Partition function, minimum free energy, nucleic acid, DNA, RNA, secondary structure, computational complexity, #P-hardness}
}
Document
DOI: 10.4230/LIPIcs.DNA.31.3
Reachability in Deletion-Only Chemical Reaction Networks

Authors: Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, and Tim Wylie

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

Abstract
For general discrete Chemical Reaction Networks (CRNs), the fundamental problem of reachability - the question of whether a target configuration can be produced from a given initial configuration - was recently shown to be Ackermann-complete. However, many open questions remain about which features of the CRN model drive this complexity. We study a restricted class of CRNs with void rules, reactions that only decrease species counts. We further examine this regime in the motivated model of step CRNs, which allow additional species to be introduced in discrete stages. With and without steps, we characterize the complexity of the reachability problem for CRNs with void rules. We show that, without steps, reachability remains polynomial-time solvable for bimolecular systems but becomes NP-complete for larger reactions. Conversely, with just a single step, reachability becomes NP-complete even for bimolecular systems. Our results provide a nearly complete classification of void-rule reachability problems into tractable and intractable cases, with only a single exception.
Cite as

Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, and Tim Wylie. Reachability in Deletion-Only Chemical Reaction Networks. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fu_et_al:LIPIcs.DNA.31.3,
  author =	{Fu, Bin and Gomez, Timothy and Knobel, Ryan and Luchsinger, Austin and Massie, Aiden and Rodriguez, Marco and Salinas, Adrian and Schweller, Robert and Wylie, Tim},
  title =	{{Reachability in Deletion-Only Chemical Reaction Networks}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{3:1--3:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.3},
  URN =		{urn:nbn:de:0030-drops-238521},
  doi =		{10.4230/LIPIcs.DNA.31.3},
  annote =	{Keywords: CRN, Chemical Reaction Network, Reachability, Void Reactions}
}
Document
DOI: 10.4230/LIPIcs.DNA.31.8
An Axiomatic Study of Leveraging Blockers to Self-Assemble Arbitrary Shapes via Temperature Programming

Authors: Matthew J. Patitz and Trent A. Rogers

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

Abstract
In this paper we present a theoretical design for tile-based self-assembling systems where individual tile sets that are universal for various tasks (e.g. building shapes or encoding arbitrary data for algorithmic systems) can be provided their input solely using sequences of variations in temperatures. Although there is prior theoretical work in so-called "temperature programming," the results presented here are based upon recent experimental work with "blocked tiles" that provides plausible evidence for their practical implementation. We develop and present an abstract mathematical model, the BlockTAM, for such systems that is based upon the experimental work, and provide constructions within it for universal number encoding systems and a universal shape building construction. These results mirror previous results in temperature programming, covering the two ends of the spectrum that seek to balance the scale factors of assemblies with the number of temperature phases required, while leveraging the features of the BlockTAM that we hope provide a pathway for future experimental implementations.
Cite as

Matthew J. Patitz and Trent A. Rogers. An Axiomatic Study of Leveraging Blockers to Self-Assemble Arbitrary Shapes via Temperature Programming. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{patitz_et_al:LIPIcs.DNA.31.8,
  author =	{Patitz, Matthew J. and Rogers, Trent A.},
  title =	{{An Axiomatic Study of Leveraging Blockers to Self-Assemble Arbitrary Shapes via Temperature Programming}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.8},
  URN =		{urn:nbn:de:0030-drops-238574},
  doi =		{10.4230/LIPIcs.DNA.31.8},
  annote =	{Keywords: DNA tiles, self-assembly, temperature programming}
}
Document
DOI: 10.4230/LIPIcs.DNA.31.9
Synchronous Versus Asynchronous Tile-Based Self-Assembly

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

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

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

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)

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@InProceedings{becker_et_al:LIPIcs.DNA.31.9,
  author =	{Becker, Florent and Drake, Phillip and Patitz, Matthew J. and Rogers, Trent A.},
  title =	{{Synchronous Versus Asynchronous Tile-Based Self-Assembly}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.9},
  URN =		{urn:nbn:de:0030-drops-238580},
  doi =		{10.4230/LIPIcs.DNA.31.9},
  annote =	{Keywords: self-assembly, noncooperative self-assembly, models of computation, tile assembly systems}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.74
Drainability and Fillability of Polyominoes in Diverse Models of Global Control

Authors: Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Tilt models offer intuitive and clean definitions of complex systems in which particles are influenced by global control commands. Despite a wide range of applications, there has been almost no theoretical investigation into the associated issues of filling and draining geometric environments. This is partly because a globally controlled system (i.e., passive matter) exhibits highly complex behavior that cannot be locally restricted. Thus, there is a strong need for theoretical studies that investigate these models both (1) in terms of relative power to each other, and (2) from a complexity theory perspective. In this work, we provide (1) general tools for comparing and contrasting different models of global control, and (2) both complexity and algorithmic results on filling and draining.
Cite as

Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer. Drainability and Fillability of Polyominoes in Diverse Models of Global Control. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 74:1-74:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fekete_et_al:LIPIcs.ICALP.2025.74,
  author =	{Fekete, S\'{a}ndor P. and Kramer, Peter and Reinhardt, Jan-Marc and Rieck, Christian and Scheffer, Christian},
  title =	{{Drainability and Fillability of Polyominoes in Diverse Models of Global Control}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{74:1--74:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.74},
  URN =		{urn:nbn:de:0030-drops-234518},
  doi =		{10.4230/LIPIcs.ICALP.2025.74},
  annote =	{Keywords: Global control, full Tilt, single Tilt, Fillability, Drainability, Polyominoes, Complexity}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.11
Hardness of Traversing Gadget Systems with Small Bandwidth

Authors: MIT Gadgets Group, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Markus Hecher, and Jayson Lynch

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

Abstract
The motion-planning-through-gadgets framework has enabled proofs of PSPACE-completeness for many motion-planning problems, ranging from swarm and modular robotics to DNA computing to video games. In this paper, we strengthen this framework to show that, for several useful gadgets and gadget families, motion planning remains PSPACE-complete even when gadgets are connected together into a graph of constant bandwidth (which implies constant pathwidth, treewidth, and cliquewidth). We then show how this result applies to several geometric/grid-based motion-planning problems, establishing PSPACE-completeness even when restricted to a rectangle/box where only one dimension is large (superconstant). On the positive side, we find one family of gadgets (DAG gadgets) for which motion planning is fixed-parameter tractable with respect to bandwidth.
Cite as

MIT Gadgets Group, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Markus Hecher, and Jayson Lynch. Hardness of Traversing Gadget Systems with Small Bandwidth. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mitgadgetsgroup_et_al:LIPIcs.SAND.2025.11,
  author =	{MIT Gadgets Group and Demaine, Erik D. and Diomidova, Jenny and Gomez, Timothy and Hecher, Markus and Lynch, Jayson},
  title =	{{Hardness of Traversing Gadget Systems with Small Bandwidth}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{11:1--11:16},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-230648},
  doi =		{10.4230/LIPIcs.SAND.2025.11},
  annote =	{Keywords: Gadgets, Motion Planning, Parameterized Complexity, Hardness}
}
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
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.23
Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks

Authors: Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, and Tim Wylie

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

Abstract
For general discrete Chemical Reaction Networks (CRNs), the fundamental problem of reachability - the question of whether a target configuration can be produced from a given initial configuration - was recently shown to be Ackermann-complete. However, many open questions remain about which features of the CRN model drive this complexity. We study a restricted class of CRNs with void rules, reactions that only decrease species counts. We further examine this regime in the motivated model of step CRNs, which allow additional species to be introduced in discrete stages. With and without steps, we characterize the complexity of the reachability problem for CRNs with void rules. We show that, without steps, reachability remains polynomial-time solvable for bimolecular systems but becomes NP-complete for larger reactions. Conversely, with just a single step, reachability becomes NP-complete even for bimolecular systems. Beyond what is contained in this brief announcement, we also investigate optimization variants of reachability, provide approximation results for maximizing species deletion, establish ETH-based lower bounds for NP-complete cases, and prove hardness for counting reaction sequences.
Cite as

Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, and Tim Wylie. Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 23:1-23:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fu_et_al:LIPIcs.SAND.2025.23,
  author =	{Fu, Bin and Gomez, Timothy and Knobel, Ryan and Luchsinger, Austin and Massie, Aiden and Rodriguez, Marco and Salinas, Adrian and Schweller, Robert and Wylie, Tim},
  title =	{{Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{23:1--23:6},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-230768},
  doi =		{10.4230/LIPIcs.SAND.2025.23},
  annote =	{Keywords: CRN, Chemical Reaction Network, Reachability, Void Reactions}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.24
Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly

Authors: Tim Gomez, Elise Grizzell, Asher Haun, Ryan Knobel, Tom Peters, Robert Schweller, and Tim Wylie

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

Abstract
The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system Γ, (b) the dynamics involved in building Γ’s assemblies, and (c) Γ’s internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile’s potential attachment or transition by selecting its state in a single step, considering all possible outcomes until the moment of selection. The system uses supertiles, each encoding the complete system being simulated. The universal system builds supertiles from its seed, each representing a single tile in Γ, transferring the information to simulate Γ to each new tile. Supertiles may also asynchronously transition states according to the rules of Γ. This result also implies IU for pairwise asynchronous Cellular Automata.
Cite as

Tim Gomez, Elise Grizzell, Asher Haun, Ryan Knobel, Tom Peters, Robert Schweller, and Tim Wylie. Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 24:1-24:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gomez_et_al:LIPIcs.SAND.2025.24,
  author =	{Gomez, Tim and Grizzell, Elise and Haun, Asher and Knobel, Ryan and Peters, Tom and Schweller, Robert and Wylie, Tim},
  title =	{{Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{24:1--24:6},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-230772},
  doi =		{10.4230/LIPIcs.SAND.2025.24},
  annote =	{Keywords: Intrinsic Universality, Tile Automata, Cellular Automata, Self-assembly}
}
Document
DOI: 10.4230/LIPIcs.DNA.30.2
Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds

Authors: Erik D. Demaine, Timothy Gomez, Elise Grizzell, Markus Hecher, Jayson Lynch, Robert Schweller, Ahmed Shalaby, and Damien Woods

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

Abstract
Molecular programmers and nanostructure engineers use domain-level design to abstract away messy DNA/RNA sequence, chemical and geometric details. Such domain-level abstractions are enforced by sequence design principles and provide a key principle that allows scaling up of complex multistranded DNA/RNA programs and structures. Determining the most favoured secondary structure, or Minimum Free Energy (MFE), of a set of strands, is typically studied at the sequence level but has seen limited domain-level work. We analyse the computational complexity of MFE for multistranded systems in a simple setting were we allow only 1 or 2 domains per strand. On the one hand, with 2-domain strands, we find that the MFE decision problem is NP-complete, even without pseudoknots, and requires exponential time algorithms assuming SAT does. On the other hand, in the simplest case of 1-domain strands there are efficient MFE algorithms for various binding modes. However, even in this single-domain case, MFE is P-hard for promiscuous binding, where one domain may bind to multiple as experimentally used by Nikitin [Nat Chem., 2023], which in turn implies that strands consisting of a single domain efficiently implement arbitrary Boolean circuits.
Cite as

Erik D. Demaine, Timothy Gomez, Elise Grizzell, Markus Hecher, Jayson Lynch, Robert Schweller, Ahmed Shalaby, and Damien Woods. Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 2:1-2:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{demaine_et_al:LIPIcs.DNA.30.2,
  author =	{Demaine, Erik D. and Gomez, Timothy and Grizzell, Elise and Hecher, Markus and Lynch, Jayson and Schweller, Robert and Shalaby, Ahmed and Woods, Damien},
  title =	{{Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{2:1--2:24},
  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.30.2},
  URN =		{urn:nbn:de:0030-drops-209304},
  doi =		{10.4230/LIPIcs.DNA.30.2},
  annote =	{Keywords: Domain-based DNA designs, minimum free energy, efficient algorithms, NP-hard, P-hard, NC, fixed-parameter tractable}
}
Document
DOI: 10.4230/LIPIcs.DNA.29.10
Complexity of Reconfiguration in Surface Chemical Reaction Networks

Authors: Robert M. Alaniz, Josh Brunner, Michael Coulombe, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Elise Grizzell, Ryan Knobel, Jayson Lynch, Andrew Rodriguez, Robert Schweller, and Tim Wylie

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

Abstract
We analyze the computational complexity of basic reconfiguration problems for the recently introduced surface Chemical Reaction Networks (sCRNs), where ordered pairs of adjacent species nondeterministically transform into a different ordered pair of species according to a predefined set of allowed transition rules (chemical reactions). In particular, two questions that are fundamental to the simulation of sCRNs are whether a given configuration of molecules can ever transform into another given configuration, and whether a given cell can ever contain a given species, given a set of transition rules. We show that these problems can be solved in polynomial time, are NP-complete, or are PSPACE-complete in a variety of different settings, including when adjacent species just swap instead of arbitrary transformation (swap sCRNs), and when cells can change species a limited number of times (k-burnout). Most problems turn out to be at least NP-hard except with very few distinct species (2 or 3).
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Robert M. Alaniz, Josh Brunner, Michael Coulombe, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Elise Grizzell, Ryan Knobel, Jayson Lynch, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Complexity of Reconfiguration in Surface Chemical Reaction Networks. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{alaniz_et_al:LIPIcs.DNA.29.10,
  author =	{Alaniz, Robert M. and Brunner, Josh and Coulombe, Michael and Demaine, Erik D. and Diomidova, Jenny and Gomez, Timothy and Grizzell, Elise and Knobel, Ryan and Lynch, Jayson and Rodriguez, Andrew and Schweller, Robert and Wylie, Tim},
  title =	{{Complexity of Reconfiguration in Surface Chemical Reaction Networks}},
  booktitle =	{29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
  pages =	{10:1--10:18},
  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.29.10},
  URN =		{urn:nbn:de:0030-drops-187936},
  doi =		{10.4230/LIPIcs.DNA.29.10},
  annote =	{Keywords: Chemical Reaction Networks, reconfiguration, hardness}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.12
Covert Computation in the Abstract Tile-Assembly Model

Authors: Robert M. Alaniz, David Caballero, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, and Tim Wylie

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
There have been many advances in molecular computation that offer benefits such as targeted drug delivery, nanoscale mapping, and improved classification of nanoscale organisms. This power led to recent work exploring privacy in the computation, specifically, covert computation in self-assembling circuits. Here, we prove several important results related to the concept of a hidden computation in the most well-known model of self-assembly, the Abstract Tile-Assembly Model (aTAM). We show that in 2D, surprisingly, the model is capable of covert computation, but only with an exponential-sized assembly. We also show that the model is capable of covert computation with polynomial-sized assemblies with only one step in the third dimension (just-barely 3D). Finally, we investigate types of functions that can be covertly computed as members of P/Poly.
Cite as

Robert M. Alaniz, David Caballero, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Covert Computation in the Abstract Tile-Assembly Model. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{alaniz_et_al:LIPIcs.SAND.2023.12,
  author =	{Alaniz, Robert M. and Caballero, David and Gomez, Timothy and Grizzell, Elise and Rodriguez, Andrew and Schweller, Robert and Wylie, Tim},
  title =	{{Covert Computation in the Abstract Tile-Assembly Model}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.12},
  URN =		{urn:nbn:de:0030-drops-179482},
  doi =		{10.4230/LIPIcs.SAND.2023.12},
  annote =	{Keywords: self-assembly, covert computation, atam}
}
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