21 Search Results for "Mimram, Samuel"

Document
DOI: 10.4230/LIPIcs.CSL.2026.21
Classifying Covering Types in Homotopy Type Theory

Authors: Samuel Mimram and Émile Oleon

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Covering spaces are a fundamental tool in algebraic topology because of the close relationship they bear with the fundamental groups of spaces. Indeed, they are in correspondence with the subgroups of the fundamental group: this is known as the Galois correspondence. In particular, the covering space corresponding to the trivial group is the universal covering, which is a "1-connected" variant of the original space, in the sense that it has the same homotopy groups, except for the first one which is trivial. In this article, we formalize this correspondence in homotopy type theory, a variant of Martin-Löf type theory in which types can be interpreted as spaces (up to homotopy). Along the way, we develop an n-dimensional generalization of covering spaces. Moreover, in order to demonstrate the applicability of our approach, we formally classify the covering of lens spaces and explain how to construct the Poincaré homology sphere.
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Samuel Mimram and Émile Oleon. Classifying Covering Types in Homotopy Type Theory. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mimram_et_al:LIPIcs.CSL.2026.21,
  author =	{Mimram, Samuel and Oleon, \'{E}mile},
  title =	{{Classifying Covering Types in Homotopy Type Theory}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.21},
  URN =		{urn:nbn:de:0030-drops-254456},
  doi =		{10.4230/LIPIcs.CSL.2026.21},
  annote =	{Keywords: homotopy type theory, covering, Galois correspondence}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.43
Kamp Theorem for Pomset Languages of Higher Dimensional Automata

Authors: Emily Clement, Enzo Erlich, and Jérémy Ledent

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially ordered multisets, or pomsets. Recent work has shown that Monadic Second Order (MSO) logic is as expressive as HDA for pomset languages. In the case of words, Kamp’s theorem states that First Order (FO) logic is as expressive as Linear Temporal Logic (LTL). In this paper, we extend this result to pomsets. To do so, we first investigate the class of pomset languages that are definable in FO. As expected, this is a strict subclass of MSO-definable languages. Then, we define a Linear Temporal Logic for pomsets (LTL_Poms), and show that it is equivalent to FO.
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Emily Clement, Enzo Erlich, and Jérémy Ledent. Kamp Theorem for Pomset Languages of Higher Dimensional Automata. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 43:1-43:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clement_et_al:LIPIcs.CSL.2026.43,
  author =	{Clement, Emily and Erlich, Enzo and Ledent, J\'{e}r\'{e}my},
  title =	{{Kamp Theorem for Pomset Languages of Higher Dimensional Automata}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{43:1--43:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.43},
  URN =		{urn:nbn:de:0030-drops-254685},
  doi =		{10.4230/LIPIcs.CSL.2026.43},
  annote =	{Keywords: Higher dimensional automata, temporal logic, Kamp’s theorem}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.30
Coherent Tietze Transformations of 1-Polygraphs in Homotopy Type Theory

Authors: Samuel Mimram and Émile Oleon

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Polygraphs play a fundamental role in algebra, geometry, and computer science, by generalizing group presentations to higher-dimensional structures and encoding coherence for those. They have recently been adapted by Kraus and von Raumer to the setting of homotopy type theory, where they are useful to define and study higher inductive types. Here, we develop the theory of 1-dimensional polygraphs, which correspond to presentations of sets in homotopy type theory. This requires us to introduce a dedicated notion of Tietze transformation, generalizing their well-known counterpart in group theory: the equivalence generated by those transformations characterizes situations where two 1-polygraphs present the same set. We also show a homotopy transfer theorem, which provides a way to transport coherence structures from one 1-polygraph to another. This work lays the foundations for a general theory of polygraphs in arbitrary dimensions, which should be useful for instance to define and study coherent group presentations, allowing for synthetic (co)homology computations. Most of the results in the article have been formalized with the Agda proof assistant using the cubical HoTT library.
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Samuel Mimram and Émile Oleon. Coherent Tietze Transformations of 1-Polygraphs in Homotopy Type Theory. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mimram_et_al:LIPIcs.FSCD.2025.30,
  author =	{Mimram, Samuel and Oleon, \'{E}mile},
  title =	{{Coherent Tietze Transformations of 1-Polygraphs in Homotopy Type Theory}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{30:1--30:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.30},
  URN =		{urn:nbn:de:0030-drops-236456},
  doi =		{10.4230/LIPIcs.FSCD.2025.30},
  annote =	{Keywords: homotopy type theory, polygraph, Tietze transformation, coherence}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.23
∞-Categorical Models of Linear Logic

Authors: Eliès Harington and Samuel Mimram

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
The notion of categorical model of linear logic is now well studied and established around the notion of linear-non-linear adjunction, which encompasses the earlier notions of Seely categories, Lafont categories and linear categories. These categorical structures have counterparts in the realm of ∞-categories, which can thus be thought of as weak forms of models of linear logic. The goal of this article is to formally introduce them and study their relationships. We show that ∞-linear-non-linear adjunctions still play the role of a unifying notion of model in this setting. Moreover, we provide a sufficient condition for a symmetric monoidal ∞-category to be Lafont. Finally, we illustrate our constructions by providing models: we construct linear-non-linear adjunctions that generalize well-known models in relations (and variants based on profunctors or spans), domains and vector spaces. In particular, we introduce a model based on spectra, a homotopical variant of abelian groups.
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Eliès Harington and Samuel Mimram. ∞-Categorical Models of Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harington_et_al:LIPIcs.FSCD.2025.23,
  author =	{Harington, Eli\`{e}s and Mimram, Samuel},
  title =	{{∞-Categorical Models of Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.23},
  URN =		{urn:nbn:de:0030-drops-236381},
  doi =		{10.4230/LIPIcs.FSCD.2025.23},
  annote =	{Keywords: linear logic, linear-non-linear adjunction, ∞-category, spectrum}
}
Artifact
Software
DOI: 10.4230/artifacts.23666
Polygraphs in Agda

Authors: Samuel Mimram

Abstract
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Samuel Mimram. Polygraphs in Agda (Software, Agda proofs). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{git,
   title = {{Polygraphs in Agda}}, 
   author = {Mimram, Samuel},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:27f2a0c3a496b72c3f4cd458ab51ea174f448eb7;origin=https://github.com/smimram/agda-polygraphs;visit=swh:1:snp:6e6d2ec50a9e996376d3965407b63e649c003f96;anchor=swh:1:rev:d3c1757f5b405f2035efda8cd825e5a53bcd6ed8}{\texttt{swh:1:dir:27f2a0c3a496b72c3f4cd458ab51ea174f448eb7}} (visited on 2025-07-07)},
   url = {https://github.com/smimram/agda-polygraphs},
   doi = {10.4230/artifacts.23666},
}
Artifact
Software
DOI: 10.4230/artifacts.22463
Delooping generated groups in homotopy type theory

Authors: Camil Champin and Samuel Mimram

Abstract
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Camil Champin, Samuel Mimram. Delooping generated groups in homotopy type theory (Software, Proofs). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22463,
   title = {{Delooping generated groups in homotopy type theory}}, 
   author = {Champin, Camil and Mimram, Samuel},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:4fc863802e40f99733703893622a7aa23c50c308;origin=https://github.com/smimram/generated-deloopings-agda;visit=swh:1:snp:209bea02bef97c56fbcc2da7af07f6b27e89b12c;anchor=swh:1:rev:6b457f58ef54a2ef8e7338fbe7d56a893cc79831}{\texttt{swh:1:dir:4fc863802e40f99733703893622a7aa23c50c308}} (visited on 2024-11-28)},
   url = {https://github.com/smimram/generated-deloopings-agda},
   doi = {10.4230/artifacts.22463},
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.6
Delooping Generated Groups in Homotopy Type Theory

Authors: Camil Champin, Samuel Mimram, and Émile Oleon

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Homotopy type theory is a logical setting based on Martin-Löf type theory in which one can perform geometric constructions and proofs in a synthetic way. Namely, types can be interpreted as spaces (up to continuous deformation) and proofs as homotopy invariant constructions. In this context, loop spaces of pointed connected groupoids provide a natural representation of groups, and any group can be obtained as the loop space of such a type, which is then called a delooping of the group. There are two main methods to construct the delooping of an arbitrary group G. The first one consists in describing it as a pointed higher inductive type, whereas the second one consists in taking the connected component of the principal G-torsor in the type of sets equipped with an action of G. We show here that, when a presentation is known for the group, simpler variants of those constructions can be used to build deloopings. The resulting types are more amenable to computations and lead to simpler meta-theoretic reasoning. We also investigate, in this context, an abstract construction for the Cayley graph of a generated group and show that it encodes the relations of the group. Most of the developments performed in the article have been formalized using the cubical version of the Agda proof assistant.
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Camil Champin, Samuel Mimram, and Émile Oleon. Delooping Generated Groups in Homotopy Type Theory. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{champin_et_al:LIPIcs.FSCD.2024.6,
  author =	{Champin, Camil and Mimram, Samuel and Oleon, \'{E}mile},
  title =	{{Delooping Generated Groups in Homotopy Type Theory}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.6},
  URN =		{urn:nbn:de:0030-drops-203356},
  doi =		{10.4230/LIPIcs.FSCD.2024.6},
  annote =	{Keywords: homotopy type theory, delooping, group, generator, Cayley graph}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.16
Categorical Coherence from Term Rewriting Systems

Authors: Samuel Mimram

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
The celebrated Squier theorem allows to prove coherence properties of algebraic structures, such as MacLane’s coherence theorem for monoidal categories, based on rewriting techniques. We are interested here in extending the theory and associated tools simultaneously in two directions. Firstly, we want to take in account situations where coherence is partial, in the sense that it only applies for a subset of structural morphisms (for instance, in the case of the coherence theorem for symmetric monoidal categories, we do not want to strictify the symmetry). Secondly, we are interested in structures where variables can be duplicated or erased. We develop theorems and rewriting techniques in order to achieve this, first in the setting of abstract rewriting systems, and then extend them to term rewriting systems, suitably generalized in order to take coherence in account. As an illustration of our results, we explain how to recover the coherence theorems for monoidal and symmetric monoidal categories.
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Samuel Mimram. Categorical Coherence from Term Rewriting Systems. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mimram:LIPIcs.FSCD.2023.16,
  author =	{Mimram, Samuel},
  title =	{{Categorical Coherence from Term Rewriting Systems}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.16},
  URN =		{urn:nbn:de:0030-drops-180009},
  doi =		{10.4230/LIPIcs.FSCD.2023.16},
  annote =	{Keywords: coherence, rewriting system, Lawvere theory}
}
Document
DOI: 10.4230/LITES.8.2.3
Higher-Dimensional Timed and Hybrid Automata

Authors: Uli Fahrenberg

Published in: LITES, Volume 8, Issue 2 (2022): Special Issue on Distributed Hybrid Systems. Leibniz Transactions on Embedded Systems, Volume 8, Issue 2

Abstract
We introduce a new formalism of higher-dimensional timed automata, based on Pratt and van Glabbeek’s higher-dimensional automata and Alur and Dill’s timed automata. We prove that their reachability is PSPACE-complete and can be decided using zone-based algorithms. We also extend the setting to higher-dimensional hybrid automata.The interest of our formalism is in modeling systems which exhibit both real-time behavior and concurrency. Other existing formalisms for real-time modeling identify concurrency and interleaving, which, as we shall argue, is problematic.
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Uli Fahrenberg. Higher-Dimensional Timed and Hybrid Automata. In LITES, Volume 8, Issue 2 (2022): Special Issue on Distributed Hybrid Systems. Leibniz Transactions on Embedded Systems, Volume 8, Issue 2, pp. 03:1-03:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{fahrenberg:LITES.8.2.3,
  author =	{Fahrenberg, Uli},
  title =	{{Higher-Dimensional Timed and Hybrid Automata}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{03:1--03:16},
  ISSN =	{2199-2002},
  year =	{2022},
  volume =	{8},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.8.2.3},
  URN =		{urn:nbn:de:0030-drops-192951},
  doi =		{10.4230/LITES.8.2.3},
  annote =	{Keywords: timed automaton, higher-dimensional automaton, precubical set, real time, non-interleaving concurrency, hybrid automaton}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2021.2
Formalisation of Dependent Type Theory: The Example of CaTT

Authors: Thibaut Benjamin

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)

Abstract
We present the type theory CaTT, originally introduced by Finster and Mimram to describe globular weak ω-categories, formalise this theory in the language of homotopy type theory and discuss connections with the open problem internalising higher structures. Most of the studies about this type theory assume that it is well-formed and satisfy the usual syntactic properties that dependent type theories enjoy, without being completely clear and thorough about what these properties are exactly. We use our formalisation to list and formally prove all of these meta-properties, thus filling a gap in the foundational aspect. We discuss the aspects of the formalisation inherent to CaTT. We present the formalisation in a way that not only handles the type theory CaTT but also related type theories that share the same structure, and in particular we show that this formalisation provides a proper ground to the study of the theory MCaTT which describes the globular monoidal weak ω-categories. The article is accompanied by a development in the proof assistant Agda to check the formalisation that we present.
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Thibaut Benjamin. Formalisation of Dependent Type Theory: The Example of CaTT. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{benjamin:LIPIcs.TYPES.2021.2,
  author =	{Benjamin, Thibaut},
  title =	{{Formalisation of Dependent Type Theory: The Example of CaTT}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{2:1--2:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.2},
  URN =		{urn:nbn:de:0030-drops-167719},
  doi =		{10.4230/LIPIcs.TYPES.2021.2},
  annote =	{Keywords: Dependent type theory, homotopy type theory, higher categories, formalisation, Agda, proof assistant}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.11
Division by Two, in Homotopy Type Theory

Authors: Samuel Mimram and Émile Oleon

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Natural numbers are isomorphism classes of finite sets and one can look for operations on sets which, after quotienting, allow recovering traditional arithmetic operations. Moreover, from a constructivist perspective, it is interesting to study whether those operations can be performed without resorting to the axiom of choice (the use of classical logic is usually necessary). Following the work of Bernstein, Sierpiński, Doyle and Conway, we study here "division by two" (or, rather, regularity of multiplication by two). We provide here a full formalization of this operation on sets, using the cubical variant of Agda, which is an implementation of the homotopy type theory setting, thus revealing some interesting points in the proof. As a novel contribution, we also show that this construction extends to general types, as opposed to sets.
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Samuel Mimram and Émile Oleon. Division by Two, in Homotopy Type Theory. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mimram_et_al:LIPIcs.FSCD.2022.11,
  author =	{Mimram, Samuel and Oleon, \'{E}mile},
  title =	{{Division by Two, in Homotopy Type Theory}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.11},
  URN =		{urn:nbn:de:0030-drops-162920},
  doi =		{10.4230/LIPIcs.FSCD.2022.11},
  annote =	{Keywords: division, axiom of choice, set theory, homotopy type theory, Agda}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2019.18
Nominal String Diagrams

Authors: Samuel Balco and Alexander Kurz

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

Abstract
We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we develop the beginnings of a theory of monoidal categories internal in a symmetric monoidal category. As an instance, we obtain a notion of a nominal PROP as a PROP internal in nominal sets. A 2-dimensional calculus of simultaneous substitutions is an application.
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Samuel Balco and Alexander Kurz. Nominal String Diagrams. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{balco_et_al:LIPIcs.CALCO.2019.18,
  author =	{Balco, Samuel and Kurz, Alexander},
  title =	{{Nominal String Diagrams}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.18},
  URN =		{urn:nbn:de:0030-drops-114466},
  doi =		{10.4230/LIPIcs.CALCO.2019.18},
  annote =	{Keywords: string diagrams, nominal sets, separated product, simultaneous substitutions, internal category, monoidal category, internal monoidal categories, PROP}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.34
A Sound Foundation for the Topological Approach to Task Solvability

Authors: Jérémy Ledent and Samuel Mimram

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
The area of fault-tolerant distributed computability is concerned with the solvability of decision tasks in various computational models where the processes might crash. A very successful approach to prove impossibility results in this context is that of combinatorial topology, started by Herlihy and Shavit’s paper in 1999. They proved that, for wait-free protocols where the processes communicate through read/write registers, a task is solvable if and only if there exists some map between simplicial complexes satisfying some properties. This approach was then extended to many different contexts, where the processes have access to various synchronization and communication primitives. Usually, in those cases, the existence of a simplicial map from the protocol complex to the output complex is taken as the definition of what it means to solve a task. In particular, no proof is provided of the fact that this abstract topological definition agrees with a more concrete operational definition of task solvability. In this paper, we bridge this gap by proving a version of Herlihy and Shavit’s theorem that applies to any kind of object. First, we start with a very general way of specifying concurrent objects, and we define what it means to implement an object B in a computational model where the processes are allowed to communicate through shared objects A_1, ..., A_k. Then, we derive the notion of a decision task as a special case of concurrent object. Finally, we prove an analogue of Herlihy and Shavit’s theorem in this context. In particular, our version of the theorem subsumes all the uses of the combinatorial topology approach that we are aware of.
Cite as

Jérémy Ledent and Samuel Mimram. A Sound Foundation for the Topological Approach to Task Solvability. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{ledent_et_al:LIPIcs.CONCUR.2019.34,
  author =	{Ledent, J\'{e}r\'{e}my and Mimram, Samuel},
  title =	{{A Sound Foundation for the Topological Approach to Task Solvability}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.34},
  URN =		{urn:nbn:de:0030-drops-109365},
  doi =		{10.4230/LIPIcs.CONCUR.2019.34},
  annote =	{Keywords: Fault-tolerant protocols, Asynchronous computability, Combinatorial topology, Protocol complex, Distributed task}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2018.28
Concurrent Specifications Beyond Linearizability

Authors: Éric Goubault, Jérémy Ledent, and Samuel Mimram

Published in: LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

Abstract
With the advent of parallel architectures, distributed programs are used intensively and the question of how to formally specify the behaviors expected from such programs becomes crucial. A very general way to specify concurrent objects is to simply give the set of all the execution traces that we consider correct for the object. In many cases, one is only interested in studying a subclass of these concurrent specifications, and more convenient tools such as linearizability can be used to describe them. In this paper, what we call a concurrent specification will be a set of execution traces that moreover satisfies a number of axioms. As we argue, these are actually the only concurrent specifications of interest: we prove that, in a reasonable computational model, every program satisfies all of our axioms. Restricting to this class of concurrent specifications allows us to formally relate our concurrent specifications with the ones obtained by linearizability, as well as its more recent variants (set- and interval-linearizability).
Cite as

Éric Goubault, Jérémy Ledent, and Samuel Mimram. Concurrent Specifications Beyond Linearizability. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{goubault_et_al:LIPIcs.OPODIS.2018.28,
  author =	{Goubault, \'{E}ric and Ledent, J\'{e}r\'{e}my and Mimram, Samuel},
  title =	{{Concurrent Specifications Beyond Linearizability}},
  booktitle =	{22nd International Conference on Principles of Distributed Systems (OPODIS 2018)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-098-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{125},
  editor =	{Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.28},
  URN =		{urn:nbn:de:0030-drops-100888},
  doi =		{10.4230/LIPIcs.OPODIS.2018.28},
  annote =	{Keywords: concurrent specification, concurrent object, linearizability}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2018.50
Brief Announcement: On the Impossibility of Detecting Concurrency

Authors: Éric Goubault, Jérémy Ledent, and Samuel Mimram

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Abstract
We identify a general principle of distributed computing: one cannot force two processes running in parallel to see each other. This principle is formally stated in the context of asynchronous processes communicating through shared objects, using trace-based semantics. We prove that it holds in a reasonable computational model, and then study the class of concurrent specifications which satisfy this property. This allows us to derive a Galois connection theorem for different variants of linearizability.
Cite as

Éric Goubault, Jérémy Ledent, and Samuel Mimram. Brief Announcement: On the Impossibility of Detecting Concurrency. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 50:1-50:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{goubault_et_al:LIPIcs.DISC.2018.50,
  author =	{Goubault, \'{E}ric and Ledent, J\'{e}r\'{e}my and Mimram, Samuel},
  title =	{{Brief Announcement: On the Impossibility of Detecting Concurrency}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{50:1--50:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.50},
  URN =		{urn:nbn:de:0030-drops-98392},
  doi =		{10.4230/LIPIcs.DISC.2018.50},
  annote =	{Keywords: concurrent specification, concurrent object, linearizability}
}
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