13 Search Results for "Roux, Pierre"

Document
DOI: 10.4230/LIPIcs.ITP.2024.30
A Coq Formalization of Taylor Models and Power Series for Solving Ordinary Differential Equations

Authors: Sewon Park and Holger Thies

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
In exact real computation real numbers are manipulated exactly without round-off errors, making it well-suited for high precision verified computation. In recent work we propose an axiomatic formalization of exact real computation in the Coq theorem prover. The formalization admits an extended extraction mechanism that lets us extract computational content from constructive parts of proofs to efficient programs built on top of AERN, a Haskell library for exact real computation. Many processes in science and engineering are modeled by ordinary differential equations (ODEs), and often safety-critical applications depend on computing their solutions correctly. The primary goal of the current work is to extend our framework to spaces of functions and to support computation of solutions to ODEs and other essential operators. In numerical mathematics, the most common way to represent continuous functions is to use polynomial approximations. This can be modeled by so-called Taylor models, that encode a function as a polynomial and a rigorous error-bound over some domain. We define types of classical functions that do not hold any computational content and formalize Taylor models to computationally approximate those classical functions. Classical functions are defined in a way to admit classical principles in their constructions and verification. We define various basic operations on Taylor models and verify their correctness based on the classical functions that they approximate. We then shift our interest to analytic functions as a generalization of Taylor models where polynomials are replaced by infinite power series. We use the formalization to develop a theory of non-linear polynomial ODEs. From the proofs we can extract certified exact real computation programs that compute solutions of ODEs on some time interval up to any precision.
Cite as

Sewon Park and Holger Thies. A Coq Formalization of Taylor Models and Power Series for Solving Ordinary Differential Equations. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{park_et_al:LIPIcs.ITP.2024.30,
  author =	{Park, Sewon and Thies, Holger},
  title =	{{A Coq Formalization of Taylor Models and Power Series for Solving Ordinary Differential Equations}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.30},
  URN =		{urn:nbn:de:0030-drops-207581},
  doi =		{10.4230/LIPIcs.ITP.2024.30},
  annote =	{Keywords: Exact real computation, Taylor models, Analytic functions, Computable analysis, Program extraction}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.4
Taming Differentiable Logics with Coq Formalisation

Authors: Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia Ślusarz, and Kathrin Stark

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to translate propositional or first-order formulae into loss functions deployed for optimisation in machine learning. At the same time, recent attempts to give programming language support for verification of neural networks showed that DLs can be used to compile verification properties to machine-learning backends. This situation is calling for stronger guarantees about the soundness of such compilers, the soundness and compositionality of DLs, and the differentiability and performance of the resulting loss functions. In this paper, we propose an approach to formalise existing DLs using the Mathematical Components library in the Coq proof assistant. Thanks to this formalisation, we are able to give uniform semantics to otherwise disparate DLs, give formal proofs to existing informal arguments, find errors in previous work, and provide formal proofs to missing conjectured properties. This work is meant as a stepping stone for the development of programming language support for verification of machine learning.
Cite as

Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia Ślusarz, and Kathrin Stark. Taming Differentiable Logics with Coq Formalisation. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{affeldt_et_al:LIPIcs.ITP.2024.4,
  author =	{Affeldt, Reynald and Bruni, Alessandro and Komendantskaya, Ekaterina and \'{S}lusarz, Natalia and Stark, Kathrin},
  title =	{{Taming Differentiable Logics with Coq Formalisation}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.4},
  URN =		{urn:nbn:de:0030-drops-207325},
  doi =		{10.4230/LIPIcs.ITP.2024.4},
  annote =	{Keywords: Machine Learning, Loss Functions, Differentiable Logics, Logic and Semantics, Interactive Theorem Proving}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.14
End-To-End Formal Verification of a Fast and Accurate Floating-Point Approximation

Authors: Florian Faissole, Paul Geneau de Lamarlière, and Guillaume Melquiond

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Designing an efficient yet accurate floating-point approximation of a mathematical function is an intricate and error-prone process. This warrants the use of formal methods, especially formal proof, to achieve some degree of confidence in the implementation. Unfortunately, the lack of automation or its poor interplay with the more manual parts of the proof makes it way too costly in practice. This article revisits the issue by proposing a methodology and some dedicated automation, and applies them to the use case of a faithful binary64 approximation of exponential. The peculiarity of this use case is that the target of the formal verification is not a simple modeling of an external code; it is an actual floating-point function defined in the logic of the Coq proof assistant, which is thus usable inside proofs once its correctness has been fully verified. This function presents all the attributes of a state-of-the-art implementation: bit-level manipulations, large tables of constants, obscure floating-point transformations, exceptional values, etc. This function has been integrated into the proof strategies of the CoqInterval library, bringing a 20× speedup with respect to the previous implementation.
Cite as

Florian Faissole, Paul Geneau de Lamarlière, and Guillaume Melquiond. End-To-End Formal Verification of a Fast and Accurate Floating-Point Approximation. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{faissole_et_al:LIPIcs.ITP.2024.14,
  author =	{Faissole, Florian and Geneau de Lamarli\`{e}re, Paul and Melquiond, Guillaume},
  title =	{{End-To-End Formal Verification of a Fast and Accurate Floating-Point Approximation}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.14},
  URN =		{urn:nbn:de:0030-drops-207420},
  doi =		{10.4230/LIPIcs.ITP.2024.14},
  annote =	{Keywords: Program verification, floating-point arithmetic, formal proof, automated reasoning, mathematical library}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.9
Switching Between Left and Right Continuity in Network Calculus

Authors: Damien Guidolin--Pina and Marc Boyer

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
The Network Calculus theory has been designed to compute upper bounds on delay and backlog in data networks. A lot of results have been developed to address different aspects. However, they are not all compatible with each other since they make different assumptions on the continuity of a core aspect of the model (the cumulative curves). However, real systems may mix several mechanisms. When modeling such a system, one has to choose one continuity hypothesis and limit the analysis to a subset of existing results. This paper addresses the continuity problem and argues formally that continuity issues are mathematical details that can be solved as long as the min-plus properties are used (minimal and maximal service, shaping). Conversely, it gives a counter-example for properties based on strict service, requiring a generalisation of the backlogged interval notion.
Cite as

Damien Guidolin--Pina and Marc Boyer. Switching Between Left and Right Continuity in Network Calculus. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guidolinpina_et_al:LIPIcs.ECRTS.2024.9,
  author =	{Guidolin--Pina, Damien and Boyer, Marc},
  title =	{{Switching Between Left and Right Continuity in Network Calculus}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.9},
  URN =		{urn:nbn:de:0030-drops-203129},
  doi =		{10.4230/LIPIcs.ECRTS.2024.9},
  annote =	{Keywords: Worst-case analysis, Real-time and embedded systems, Network Calculus}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2022.7
An Irrelevancy-Eliminating Translation of Pure Type Systems

Authors: Nathan Mull

Published in: LIPIcs, Volume 269, 28th International Conference on Types for Proofs and Programs (TYPES 2022)

Abstract
I present an infinite-reduction-path-preserving typability-preserving translation of pure type systems which eliminates rules and sorts that are in some sense irrelevant with respect to normalization. This translation can be bootstrapped with existing results for the Barendregt-Geuvers-Klop conjecture, extending the conjecture to a larger class of systems. Performing this bootstrapping with the results of Barthe et al. [Barthe et al., 2001] yields a new class of systems with dependent rules and non-negatable sorts for which the conjecture holds. To my knowledge, this is the first improvement in the state of the conjecture since the results of Roux and van Doorn [Roux and Doorn, 2014] (which can be used for the same sort of bootstrapping argument) albeit a somewhat modest one; in essence, the translation eliminates clutter in the system that does not affect normalization. This work is done in the framework of tiered pure type systems, a simple class of persistent systems which is sufficient to study when concerned with questions about normalization.
Cite as

Nathan Mull. An Irrelevancy-Eliminating Translation of Pure Type Systems. In 28th International Conference on Types for Proofs and Programs (TYPES 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 269, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mull:LIPIcs.TYPES.2022.7,
  author =	{Mull, Nathan},
  title =	{{An Irrelevancy-Eliminating Translation of Pure Type Systems}},
  booktitle =	{28th International Conference on Types for Proofs and Programs (TYPES 2022)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-285-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{269},
  editor =	{Kesner, Delia and P\'{e}drot, Pierre-Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2022.7},
  URN =		{urn:nbn:de:0030-drops-184501},
  doi =		{10.4230/LIPIcs.TYPES.2022.7},
  annote =	{Keywords: pure type systems, normalization, reduction-path-preserving translations, Barendregt-Geuvers-Klop conjecture}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2022.3
The True Colors of Memory: A Tour of Chromatic-Memory Strategies in Zero-Sum Games on Graphs (Invited Talk)

Authors: Patricia Bouyer, Mickael Randour, and Pierre Vandenhove

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
Two-player turn-based zero-sum games on (finite or infinite) graphs are a central framework in theoretical computer science - notably as a tool for controller synthesis, but also due to their connection with logic and automata theory. A crucial challenge in the field is to understand how complex strategies need to be to play optimally, given a type of game and a winning objective. In this invited contribution, we give a tour of recent advances aiming to characterize games where finite-memory strategies suffice (i.e., using a limited amount of information about the past). We mostly focus on so-called chromatic memory, which is limited to using colors - the basic building blocks of objectives - seen along a play to update itself. Chromatic memory has the advantage of being usable in different game graphs, and the corresponding class of strategies turns out to be of great interest to both the practical and the theoretical sides.
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Patricia Bouyer, Mickael Randour, and Pierre Vandenhove. The True Colors of Memory: A Tour of Chromatic-Memory Strategies in Zero-Sum Games on Graphs (Invited Talk). In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bouyer_et_al:LIPIcs.FSTTCS.2022.3,
  author =	{Bouyer, Patricia and Randour, Mickael and Vandenhove, Pierre},
  title =	{{The True Colors of Memory: A Tour of Chromatic-Memory Strategies in Zero-Sum Games on Graphs}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.3},
  URN =		{urn:nbn:de:0030-drops-173957},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.3},
  annote =	{Keywords: two-player games on graphs, finite-memory strategies, chromatic memory, parity automata, \omega-regularity}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2022.5
A Formal Link Between Response Time Analysis and Network Calculus

Authors: Pierre Roux, Sophie Quinton, and Marc Boyer

Published in: LIPIcs, Volume 231, 34th Euromicro Conference on Real-Time Systems (ECRTS 2022)

Abstract
Classical Response Time Analysis (RTA) and Network Calculus (NC) are two major formalisms used for the verification of real-time properties. We offer mathematical links between these two different theories. Based on these links, we then prove the equivalence of various key notions in both frameworks. This enables specialists of both formalisms to get increase confidence on their models, or even, like the authors, to discover errors in theorems by investigating apparent discrepancies between some notions expected to be equivalent. The presented mathematical results are all mechanically checked with the interactive theorem prover Coq, building on existing formalizations of RTA and NC. Establishing such a link between NC and RTA paves the way for improved real-time analyses obtained by combining both theories to enjoy their respective strengths (e.g., multicore analyses for RTA or clock drifts for NC).
Cite as

Pierre Roux, Sophie Quinton, and Marc Boyer. A Formal Link Between Response Time Analysis and Network Calculus. In 34th Euromicro Conference on Real-Time Systems (ECRTS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 231, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{roux_et_al:LIPIcs.ECRTS.2022.5,
  author =	{Roux, Pierre and Quinton, Sophie and Boyer, Marc},
  title =	{{A Formal Link Between Response Time Analysis and Network Calculus}},
  booktitle =	{34th Euromicro Conference on Real-Time Systems (ECRTS 2022)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-239-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{231},
  editor =	{Maggio, Martina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2022.5},
  URN =		{urn:nbn:de:0030-drops-163224},
  doi =		{10.4230/LIPIcs.ECRTS.2022.5},
  annote =	{Keywords: Response Time Analysis, Network Calculus, dense time, discrete time, response time, formal proof, Coq}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2022.19
Foundational Response-Time Analysis as Explainable Evidence of Timeliness

Authors: Marco Maida, Sergey Bozhko, and Björn B. Brandenburg

Published in: LIPIcs, Volume 231, 34th Euromicro Conference on Real-Time Systems (ECRTS 2022)

Abstract
The paper introduces foundational response-time analysis (RTA) as a means to produce strong and independently checkable evidence of temporal correctness. In a foundational RTA, each response-time bound calculated comes with an auto-generated certificate of correctness - a short and human-inspectable sequence of machine-checked proofs that formally show the claimed bound to hold. In other words, a foundational RTA yields explainable results that can be independently verified (e.g., by a certification authority) in a rigorous manner (with an automated proof checker). Consequently, the analysis tool itself does not need to be verified nor trusted. As a proof of concept, the paper presents POET, the first foundational RTA tool. POET generates certificates based on Prosa, the to-date largest verified framework for schedulability analysis, which is based on Coq. The trusted computing base is hence reduced to the Coq proof checker and its dependencies. POET currently supports two scheduling policies (earliest-deadline-first, fixed-priority), two preemption models (fully preemptive, fully non-preemptive), arbitrary deadlines, periodic and sporadic tasks, and tasks characterized by arbitrary arrival curves. The paper describes the challenges inherent in the development of a foundational RTA tool, discusses key design choices, and reports on its scalability.
Cite as

Marco Maida, Sergey Bozhko, and Björn B. Brandenburg. Foundational Response-Time Analysis as Explainable Evidence of Timeliness. In 34th Euromicro Conference on Real-Time Systems (ECRTS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 231, pp. 19:1-19:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{maida_et_al:LIPIcs.ECRTS.2022.19,
  author =	{Maida, Marco and Bozhko, Sergey and Brandenburg, Bj\"{o}rn B.},
  title =	{{Foundational Response-Time Analysis as Explainable Evidence of Timeliness}},
  booktitle =	{34th Euromicro Conference on Real-Time Systems (ECRTS 2022)},
  pages =	{19:1--19:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-239-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{231},
  editor =	{Maggio, Martina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2022.19},
  URN =		{urn:nbn:de:0030-drops-163363},
  doi =		{10.4230/LIPIcs.ECRTS.2022.19},
  annote =	{Keywords: hard real-time systems, response-time analysis, uniprocessor, Coq, Prosa, fixed priority, EDF, preemptive, non-preemptive, verification}
}
Document
Artifact
DOI: 10.4230/DARTS.8.1.3
A Formal Link Between Response Time Analysis and Network Calculus (Artifact)

Authors: Pierre Roux, Sophie Quinton, and Marc Boyer

Published in: DARTS, Volume 8, Issue 1, Special Issue of the 34th Euromicro Conference on Real-Time Systems (ECRTS 2022)

Abstract
Classical Response Time Analysis (RTA) and Network Calculus (NC) are two major formalisms used for the verification of real-time properties. The related paper offer mathematical links between these two different theories. Based on these links, it then proves the equivalence of various key notions in both frameworks. This enables specialists of both formalisms to get increase confidence on their models, or even, like the authors, to discover errors in theorems by investigating apparent discrepancies between some notions expected to be equivalent. The presented mathematical results are all mechanically checked with the interactive theorem prover Coq, building on existing formalizations of RTA and NC. Establishing such a link between NC and RTA paves the way for improved real-time analyses obtained by combining both theories to enjoy their respective strengths (e.g., multicore analyses for RTA or clock drifts for NC). This artifact enables to reproduce these proofs.
Cite as

Pierre Roux, Sophie Quinton, and Marc Boyer. A Formal Link Between Response Time Analysis and Network Calculus (Artifact). In Special Issue of the 34th Euromicro Conference on Real-Time Systems (ECRTS 2022). Dagstuhl Artifacts Series (DARTS), Volume 8, Issue 1, pp. 3:1-3:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{roux_et_al:DARTS.8.1.3,
  author =	{Roux, Pierre and Quinton, Sophie and Boyer, Marc},
  title =	{{A Formal Link Between Response Time Analysis and Network Calculus (Artifact)}},
  pages =	{3:1--3:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2022},
  volume =	{8},
  number =	{1},
  editor =	{Roux, Pierre and Quinton, Sophie and Boyer, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.8.1.3},
  URN =		{urn:nbn:de:0030-drops-164990},
  doi =		{10.4230/DARTS.8.1.3},
  annote =	{Keywords: Response Time Analysis, Network Calculus, dense time, discrete time, response time, formal proof, Coq}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2021.14
A Residual Service Curve of Rate-Latency Server Used by Sporadic Flows Computable in Quadratic Time for Network Calculus

Authors: Marc Boyer, Pierre Roux, Hugo Daigmorte, and David Puechmaille

Published in: LIPIcs, Volume 196, 33rd Euromicro Conference on Real-Time Systems (ECRTS 2021)

Abstract
Computing response times for resources shared by periodic workloads (tasks or data flows) can be very time consuming as it depends on the least common multiple of the periods. In a previous study, a quadratic algorithm was provided to upper bound the response time of a set of periodic tasks with a fixed-priority scheduling. This paper generalises this result by considering a rate-latency server and sporadic workloads and gives a response time and residual curve that can be used in other contexts. It also provides a formal proof in the Coq language.
Cite as

Marc Boyer, Pierre Roux, Hugo Daigmorte, and David Puechmaille. A Residual Service Curve of Rate-Latency Server Used by Sporadic Flows Computable in Quadratic Time for Network Calculus. In 33rd Euromicro Conference on Real-Time Systems (ECRTS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 196, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{boyer_et_al:LIPIcs.ECRTS.2021.14,
  author =	{Boyer, Marc and Roux, Pierre and Daigmorte, Hugo and Puechmaille, David},
  title =	{{A Residual Service Curve of Rate-Latency Server Used by Sporadic Flows Computable in Quadratic Time for Network Calculus}},
  booktitle =	{33rd Euromicro Conference on Real-Time Systems (ECRTS 2021)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-192-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{196},
  editor =	{Brandenburg, Bj\"{o}rn B.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2021.14},
  URN =		{urn:nbn:de:0030-drops-139457},
  doi =		{10.4230/LIPIcs.ECRTS.2021.14},
  annote =	{Keywords: Network Calculus, response time, residual curve, rate-latency server, sporadic workload, formal proof, Coq}
}
Document
Artifact
DOI: 10.4230/DARTS.7.1.2
A Residual Service Curve of Rate-Latency Server Used by Sporadic Flows Computable in Quadratic Time for Network Calculus (Artifact)

Authors: Marc Boyer, Pierre Roux, Hugo Daigmorte, and David Puechmaille

Published in: DARTS, Volume 7, Issue 1, Special Issue of the 33rd Euromicro Conference on Real-Time Systems (ECRTS 2021)

Abstract
Computing response times for resources shared by periodic workloads (tasks or data flows) can be very time consuming as it depends on the least common multiple of the periods. In a previous study, a quadratic algorithm was provided to upper bound the response time of a set of periodic tasks with a fixed-priority scheduling. The related paper generalises this result by considering a rate-latency server and sporadic workloads and gives a response time and residual curve that can be used in other contexts. It also provides a formal proof in the Coq language. This artifact enables to reproduce this proof.
Cite as

Marc Boyer, Pierre Roux, Hugo Daigmorte, and David Puechmaille. A Residual Service Curve of Rate-Latency Server Used by Sporadic Flows Computable in Quadratic Time for Network Calculus (Artifact). In Special Issue of the 33rd Euromicro Conference on Real-Time Systems (ECRTS 2021). Dagstuhl Artifacts Series (DARTS), Volume 7, Issue 1, pp. 2:1-2:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{boyer_et_al:DARTS.7.1.2,
  author =	{Boyer, Marc and Roux, Pierre and Daigmorte, Hugo and Puechmaille, David},
  title =	{{A Residual Service Curve of Rate-Latency Server Used by Sporadic Flows Computable in Quadratic Time for Network Calculus (Artifact)}},
  pages =	{2:1--2:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2021},
  volume =	{7},
  number =	{1},
  editor =	{Boyer, Marc and Roux, Pierre and Daigmorte, Hugo and Puechmaille, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.7.1.2},
  URN =		{urn:nbn:de:0030-drops-139810},
  doi =		{10.4230/DARTS.7.1.2},
  annote =	{Keywords: Network Calculus, response time, residual curve, rate-latency server, sporadic workload, formal proof, Coq}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.24
Games Where You Can Play Optimally with Arena-Independent Finite Memory

Authors: Patricia Bouyer, Stéphane Le Roux, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
For decades, two-player (antagonistic) games on graphs have been a framework of choice for many important problems in theoretical computer science. A notorious one is controller synthesis, which can be rephrased through the game-theoretic metaphor as the quest for a winning strategy of the system in a game against its antagonistic environment. Depending on the specification, optimal strategies might be simple or quite complex, for example having to use (possibly infinite) memory. Hence, research strives to understand which settings allow for simple strategies. In 2005, Gimbert and Zielonka [Hugo Gimbert and Wieslaw Zielonka, 2005] provided a complete characterization of preference relations (a formal framework to model specifications and game objectives) that admit memoryless optimal strategies for both players. In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory - finite or infinite - is almost always required. Despite much effort, the exact frontiers of the class of preference relations that admit finite-memory optimal strategies still elude us. In this work, we establish a complete characterization of preference relations that admit optimal strategies using arena-independent finite memory, generalizing the work of Gimbert and Zielonka to the finite-memory case. We also prove an equivalent to their celebrated corollary of great practical interest: if both players have optimal (arena-independent-)finite-memory strategies in all one-player games, then it is also the case in all two-player games. Finally, we pinpoint the boundaries of our results with regard to the literature: our work completely covers the case of arena-independent memory (e.g., multiple parity objectives, lower- and upper-bounded energy objectives), and paves the way to the arena-dependent case (e.g., multiple lower-bounded energy objectives).
Cite as

Patricia Bouyer, Stéphane Le Roux, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove. Games Where You Can Play Optimally with Arena-Independent Finite Memory. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bouyer_et_al:LIPIcs.CONCUR.2020.24,
  author =	{Bouyer, Patricia and Le Roux, St\'{e}phane and Oualhadj, Youssouf and Randour, Mickael and Vandenhove, Pierre},
  title =	{{Games Where You Can Play Optimally with Arena-Independent Finite Memory}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.24},
  URN =		{urn:nbn:de:0030-drops-128360},
  doi =		{10.4230/LIPIcs.CONCUR.2020.24},
  annote =	{Keywords: two-player games on graphs, finite-memory determinacy, optimal strategies}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.7
Primitive Floats in Coq

Authors: Guillaume Bertholon, Érik Martin-Dorel, and Pierre Roux

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
Some mathematical proofs involve intensive computations, for instance: the four-color theorem, Hales' theorem on sphere packing (formerly known as the Kepler conjecture) or interval arithmetic. For numerical computations, floating-point arithmetic enjoys widespread usage thanks to its efficiency, despite the introduction of rounding errors. Formal guarantees can be obtained on floating-point algorithms based on the IEEE 754 standard, which precisely specifies floating-point arithmetic and its rounding modes, and a proof assistant such as Coq, that enjoys efficient computation capabilities. Coq offers machine integers, however floating-point arithmetic still needed to be emulated using these integers. A modified version of Coq is presented that enables using the machine floating-point operators. The main obstacles to such an implementation and its soundness are discussed. Benchmarks show potential performance gains of two orders of magnitude.
Cite as

Guillaume Bertholon, Érik Martin-Dorel, and Pierre Roux. Primitive Floats in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bertholon_et_al:LIPIcs.ITP.2019.7,
  author =	{Bertholon, Guillaume and Martin-Dorel, \'{E}rik and Roux, Pierre},
  title =	{{Primitive Floats in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.7},
  URN =		{urn:nbn:de:0030-drops-110629},
  doi =		{10.4230/LIPIcs.ITP.2019.7},
  annote =	{Keywords: Coq formal proofs, floating-point arithmetic, reflexive tactics, Cholesky decomposition}
}
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