11 Search Results for "Grizzell, Elise"

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.
Cite as

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
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.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).
Cite as

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}
}
Document
DOI: 10.4230/LIPIcs.SAND.2022.6
Building Squares with Optimal State Complexity in Restricted Active Self-Assembly

Authors: Robert M. Alaniz, David Caballero, Sonya C. Cirlos, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, Armando Tenorio, and Tim Wylie

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model has been shown to be powerful, but many fundamental questions have yet to be explored. Here, we study the state complexity of assembling n × n squares in seeded Tile Automata systems where growth starts from a seed and tiles may attach one at a time, similar to the abstract Tile Assembly Model. We provide optimal bounds for three classes of seeded Tile Automata systems (all without detachment), which vary in the amount of complexity allowed in the transition rules. We show that, in general, seeded Tile Automata systems require Θ(log^{1/4} n) states. For Single-Transition systems, where only one state may change in a transition rule, we show a bound of Θ(log^{1/3} n), and for deterministic systems, where each pair of states may only have one associated transition rule, a bound of Θ(({log n}/{log log n})^{1/2}).
Cite as

Robert M. Alaniz, David Caballero, Sonya C. Cirlos, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, Armando Tenorio, and Tim Wylie. Building Squares with Optimal State Complexity in Restricted Active Self-Assembly. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alaniz_et_al:LIPIcs.SAND.2022.6,
  author =	{Alaniz, Robert M. and Caballero, David and Cirlos, Sonya C. and Gomez, Timothy and Grizzell, Elise and Rodriguez, Andrew and Schweller, Robert and Tenorio, Armando and Wylie, Tim},
  title =	{{Building Squares with Optimal State Complexity in Restricted Active Self-Assembly}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.6},
  URN =		{urn:nbn:de:0030-drops-159482},
  doi =		{10.4230/LIPIcs.SAND.2022.6},
  annote =	{Keywords: Active Self-Assembly, State Complexity, Tile Automata}
}
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