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Documents authored by Meunier, Pierre-Étienne

Found 2 Possible Name Variants:

Meunier, Pierre-Etienne

Document
DOI: 10.4230/LIPIcs.DNA.27.6
Directed Non-Cooperative Tile Assembly Is Decidable

Authors: Pierre-Étienne Meunier and Damien Regnault

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

Abstract
We provide a complete characterisation of all final states of a model called directed non-cooperative tile self-assembly, also called directed temperature 1 tile assembly, which proves that this model cannot possibly perform Turing computation. This model is a deterministic version of the more general undirected model, whose computational power is still open. Our result uses recent results in the domain, and solves a conjecture formalised in 2011. We believe that this is a major step towards understanding the full model. Temperature 1 tile assembly can be seen as a two-dimensional extension of finite automata, where geometry provides a form of memory and synchronisation, yet the full power of these "geometric blockings" was still largely unknown until recently (note that nontrivial algorithms which are able to build larger structures than the naive constructions have been found).
Cite as

Pierre-Étienne Meunier and Damien Regnault. Directed Non-Cooperative Tile Assembly Is Decidable. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{meunier_et_al:LIPIcs.DNA.27.6,
  author =	{Meunier, Pierre-\'{E}tienne and Regnault, Damien},
  title =	{{Directed Non-Cooperative Tile Assembly Is Decidable}},
  booktitle =	{27th International Conference on DNA Computing and Molecular Programming (DNA 27)},
  pages =	{6:1--6:21},
  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.27.6},
  URN =		{urn:nbn:de:0030-drops-146735},
  doi =		{10.4230/LIPIcs.DNA.27.6},
  annote =	{Keywords: Self-assembly, Molecular Computing, Models of Computation, Computational Geometry}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.23
Proving the Turing Universality of Oritatami Co-Transcriptional Folding

Authors: Cody Geary, Pierre-Étienne Meunier, Nicolas Schabanel, and Shinnosuke Seki

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We study the oritatami model for molecular co-transcriptional folding. In oritatami systems, the transcript (the "molecule") folds as it is synthesized (transcribed), according to a local energy optimisation process, which is similar to how actual biomolecules such as RNA fold into complex shapes and functions as they are transcribed. We prove that there is an oritatami system embedding universal computation in the folding process itself. Our result relies on the development of a generic toolbox, which is easily reusable for future work to design complex functions in oritatami systems. We develop "low-level" tools that allow to easily spread apart the encoding of different "functions" in the transcript, even if they are required to be applied at the same geometrical location in the folding. We build upon these low-level tools, a programming framework with increasing levels of abstraction, from encoding of instructions into the transcript to logical analysis. This framework is similar to the hardware-to-algorithm levels of abstractions in standard algorithm theory. These various levels of abstractions allow to separate the proof of correctness of the global behavior of our system, from the proof of correctness of its implementation. Thanks to this framework, we were able to computerise the proof of correctness of its implementation and produce certificates, in the form of a relatively small number of proof trees, compact and easily readable/checkable by human, while encapsulating huge case enumerations. We believe this particular type of certificates can be generalised to other discrete dynamical systems, where proofs involve large case enumerations as well.
Cite as

Cody Geary, Pierre-Étienne Meunier, Nicolas Schabanel, and Shinnosuke Seki. Proving the Turing Universality of Oritatami Co-Transcriptional Folding. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{geary_et_al:LIPIcs.ISAAC.2018.23,
  author =	{Geary, Cody and Meunier, Pierre-\'{E}tienne and Schabanel, Nicolas and Seki, Shinnosuke},
  title =	{{Proving the Turing Universality of Oritatami Co-Transcriptional Folding}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{23:1--23:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.23},
  URN =		{urn:nbn:de:0030-drops-99715},
  doi =		{10.4230/LIPIcs.ISAAC.2018.23},
  annote =	{Keywords: Molecular computing, Turing universality, co-transcriptional folding}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.43
Programming Biomolecules That Fold Greedily During Transcription

Authors: Cody Geary, Pierre-Etienne Meunier, Nicolas Schabanel, and Shinnosuke Seki

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
We introduce and study the computational power of Oritatami, a theoretical model to explore greedy molecular folding, by which a molecule begins to fold before awaiting the end of its production. This model is inspired by a recent experimental work demonstrating the construction of shapes at the nanoscale by folding an RNA molecule during its transcription from an engineered sequence of synthetic DNA. An important challenge of this model, also encountered in experiments, is to get a single sequence to fold into different shapes, depending on the surrounding molecules. Another big challenge is that not all parts of the sequence are meaningful for all possible inputs. Hence, to prevent them from interfering with subsequent operations in the Oritatami folding pathway we must structure the unused portions of the sequence depending on the context in which it folds. Next, we introduce general design techniques to solve these challenges and program molecules. Our main result in this direction is an algorithm that is time linear in the sequence length that finds a rule for folding the sequence deterministically into a prescribed set of shapes, dependent on its local environment. This shows that the corresponding problem is fixed-parameter tractable, although we also prove it NP-complete in the number of possible environments.
Cite as

Cody Geary, Pierre-Etienne Meunier, Nicolas Schabanel, and Shinnosuke Seki. Programming Biomolecules That Fold Greedily During Transcription. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{geary_et_al:LIPIcs.MFCS.2016.43,
  author =	{Geary, Cody and Meunier, Pierre-Etienne and Schabanel, Nicolas and Seki, Shinnosuke},
  title =	{{Programming Biomolecules That Fold Greedily During Transcription}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.43},
  URN =		{urn:nbn:de:0030-drops-64567},
  doi =		{10.4230/LIPIcs.MFCS.2016.43},
  annote =	{Keywords: natural computing, self-assembly, molecular folding}
}

Meunier, Pierre-Étienne

Document
DOI: 10.4230/LIPIcs.DNA.27.6
Directed Non-Cooperative Tile Assembly Is Decidable

Authors: Pierre-Étienne Meunier and Damien Regnault

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

Abstract
We provide a complete characterisation of all final states of a model called directed non-cooperative tile self-assembly, also called directed temperature 1 tile assembly, which proves that this model cannot possibly perform Turing computation. This model is a deterministic version of the more general undirected model, whose computational power is still open. Our result uses recent results in the domain, and solves a conjecture formalised in 2011. We believe that this is a major step towards understanding the full model. Temperature 1 tile assembly can be seen as a two-dimensional extension of finite automata, where geometry provides a form of memory and synchronisation, yet the full power of these "geometric blockings" was still largely unknown until recently (note that nontrivial algorithms which are able to build larger structures than the naive constructions have been found).
Cite as

Pierre-Étienne Meunier and Damien Regnault. Directed Non-Cooperative Tile Assembly Is Decidable. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{meunier_et_al:LIPIcs.DNA.27.6,
  author =	{Meunier, Pierre-\'{E}tienne and Regnault, Damien},
  title =	{{Directed Non-Cooperative Tile Assembly Is Decidable}},
  booktitle =	{27th International Conference on DNA Computing and Molecular Programming (DNA 27)},
  pages =	{6:1--6:21},
  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.27.6},
  URN =		{urn:nbn:de:0030-drops-146735},
  doi =		{10.4230/LIPIcs.DNA.27.6},
  annote =	{Keywords: Self-assembly, Molecular Computing, Models of Computation, Computational Geometry}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.23
Proving the Turing Universality of Oritatami Co-Transcriptional Folding

Authors: Cody Geary, Pierre-Étienne Meunier, Nicolas Schabanel, and Shinnosuke Seki

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We study the oritatami model for molecular co-transcriptional folding. In oritatami systems, the transcript (the "molecule") folds as it is synthesized (transcribed), according to a local energy optimisation process, which is similar to how actual biomolecules such as RNA fold into complex shapes and functions as they are transcribed. We prove that there is an oritatami system embedding universal computation in the folding process itself. Our result relies on the development of a generic toolbox, which is easily reusable for future work to design complex functions in oritatami systems. We develop "low-level" tools that allow to easily spread apart the encoding of different "functions" in the transcript, even if they are required to be applied at the same geometrical location in the folding. We build upon these low-level tools, a programming framework with increasing levels of abstraction, from encoding of instructions into the transcript to logical analysis. This framework is similar to the hardware-to-algorithm levels of abstractions in standard algorithm theory. These various levels of abstractions allow to separate the proof of correctness of the global behavior of our system, from the proof of correctness of its implementation. Thanks to this framework, we were able to computerise the proof of correctness of its implementation and produce certificates, in the form of a relatively small number of proof trees, compact and easily readable/checkable by human, while encapsulating huge case enumerations. We believe this particular type of certificates can be generalised to other discrete dynamical systems, where proofs involve large case enumerations as well.
Cite as

Cody Geary, Pierre-Étienne Meunier, Nicolas Schabanel, and Shinnosuke Seki. Proving the Turing Universality of Oritatami Co-Transcriptional Folding. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{geary_et_al:LIPIcs.ISAAC.2018.23,
  author =	{Geary, Cody and Meunier, Pierre-\'{E}tienne and Schabanel, Nicolas and Seki, Shinnosuke},
  title =	{{Proving the Turing Universality of Oritatami Co-Transcriptional Folding}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{23:1--23:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.23},
  URN =		{urn:nbn:de:0030-drops-99715},
  doi =		{10.4230/LIPIcs.ISAAC.2018.23},
  annote =	{Keywords: Molecular computing, Turing universality, co-transcriptional folding}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.43
Programming Biomolecules That Fold Greedily During Transcription

Authors: Cody Geary, Pierre-Etienne Meunier, Nicolas Schabanel, and Shinnosuke Seki

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
We introduce and study the computational power of Oritatami, a theoretical model to explore greedy molecular folding, by which a molecule begins to fold before awaiting the end of its production. This model is inspired by a recent experimental work demonstrating the construction of shapes at the nanoscale by folding an RNA molecule during its transcription from an engineered sequence of synthetic DNA. An important challenge of this model, also encountered in experiments, is to get a single sequence to fold into different shapes, depending on the surrounding molecules. Another big challenge is that not all parts of the sequence are meaningful for all possible inputs. Hence, to prevent them from interfering with subsequent operations in the Oritatami folding pathway we must structure the unused portions of the sequence depending on the context in which it folds. Next, we introduce general design techniques to solve these challenges and program molecules. Our main result in this direction is an algorithm that is time linear in the sequence length that finds a rule for folding the sequence deterministically into a prescribed set of shapes, dependent on its local environment. This shows that the corresponding problem is fixed-parameter tractable, although we also prove it NP-complete in the number of possible environments.
Cite as

Cody Geary, Pierre-Etienne Meunier, Nicolas Schabanel, and Shinnosuke Seki. Programming Biomolecules That Fold Greedily During Transcription. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{geary_et_al:LIPIcs.MFCS.2016.43,
  author =	{Geary, Cody and Meunier, Pierre-Etienne and Schabanel, Nicolas and Seki, Shinnosuke},
  title =	{{Programming Biomolecules That Fold Greedily During Transcription}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.43},
  URN =		{urn:nbn:de:0030-drops-64567},
  doi =		{10.4230/LIPIcs.MFCS.2016.43},
  annote =	{Keywords: natural computing, self-assembly, molecular folding}
}
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