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Documents authored by Ghyselen, Alexis

Document
DOI: 10.4230/LIPIcs.CSL.2023.17
Open Higher-Order Logic

Authors: Ugo Dal Lago, Francesco Gavazzo, and Alexis Ghyselen

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
We introduce a variation on Barthe et al.’s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity, differentiability, or monotonicity, can be expressed and reasoned about in a very natural way, following the structure of the underlying program. We give open higher-order logic in distinct flavors, and in particular in its relational and local versions, the latter being tailored for situations in which properties hold only in part of the underlying function’s domain of definition.
Cite as

Ugo Dal Lago, Francesco Gavazzo, and Alexis Ghyselen. Open Higher-Order Logic. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dallago_et_al:LIPIcs.CSL.2023.17,
  author =	{Dal Lago, Ugo and Gavazzo, Francesco and Ghyselen, Alexis},
  title =	{{Open Higher-Order Logic}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.17},
  URN =		{urn:nbn:de:0030-drops-174785},
  doi =		{10.4230/LIPIcs.CSL.2023.17},
  annote =	{Keywords: Formal Verification, Relational Logic, First-Order Properties}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.34
Sized Types with Usages for Parallel Complexity of Pi-Calculus Processes

Authors: Patrick Baillot, Alexis Ghyselen, and Naoki Kobayashi

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
We address the problem of analysing the complexity of concurrent programs written in Pi-calculus. We are interested in parallel complexity, or span, understood as the execution time in a model with maximal parallelism. A type system for parallel complexity has been recently proposed by the first two authors but it is too imprecise for non-linear channels and cannot analyse some concurrent processes. Aiming for a more precise analysis, we design a type system which builds on the concepts of sized types and usages. The sized types allow us to parametrize the complexity by the size of inputs, and the usages allow us to achieve a kind of rely-guarantee reasoning on the timing each process communicates with its environment. We prove that our new type system soundly estimates the parallel complexity, and show through examples that it is often more precise than the previous type system of the first two authors.
Cite as

Patrick Baillot, Alexis Ghyselen, and Naoki Kobayashi. Sized Types with Usages for Parallel Complexity of Pi-Calculus Processes. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 34:1-34:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baillot_et_al:LIPIcs.CONCUR.2021.34,
  author =	{Baillot, Patrick and Ghyselen, Alexis and Kobayashi, Naoki},
  title =	{{Sized Types with Usages for Parallel Complexity of Pi-Calculus Processes}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{34:1--34:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.34},
  URN =		{urn:nbn:de:0030-drops-144111},
  doi =		{10.4230/LIPIcs.CONCUR.2021.34},
  annote =	{Keywords: Type Systems, Pi-calculus, Process Calculi, Complexity Analysis, Usages, Sized Types}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.9
Combining Linear Logic and Size Types for Implicit Complexity

Authors: Patrick Baillot and Alexis Ghyselen

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Several type systems have been proposed to statically control the time complexity of lambda-calculus programs and characterize complexity classes such as FPTIME or FEXPTIME. A first line of research stems from linear logic and restricted versions of its !-modality controlling duplication. A second approach relies on the idea of tracking the size increase between input and output, and together with a restricted recursion scheme, to deduce time complexity bounds. However both approaches suffer from limitations : either a limited intensional expressivity, or linearity restrictions. In the present work we incorporate both approaches into a common type system, in order to overcome their respective constraints. Our system is based on elementary linear logic combined with linear size types, called sEAL, and leads to characterizations of the complexity classes FPTIME and 2k-FEXPTIME, for k >= 0.
Cite as

Patrick Baillot and Alexis Ghyselen. Combining Linear Logic and Size Types for Implicit Complexity. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baillot_et_al:LIPIcs.CSL.2018.9,
  author =	{Baillot, Patrick and Ghyselen, Alexis},
  title =	{{Combining Linear Logic and Size Types for Implicit Complexity}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.9},
  URN =		{urn:nbn:de:0030-drops-96763},
  doi =		{10.4230/LIPIcs.CSL.2018.9},
  annote =	{Keywords: Implicit computational complexity, lambda-calculus, linear logic, type systems, polynomial time complexity, size types}
}
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