12 Search Results for "Roux, Pierre"


Document
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
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.

Cite as

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
Artifact
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
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
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
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
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
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
A Verified LL(1) Parser Generator

Authors: Sam Lasser, Chris Casinghino, Kathleen Fisher, and Cody Roux

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


Abstract
An LL(1) parser is a recursive descent algorithm that uses a single token of lookahead to build a grammatical derivation for an input sequence. We present an LL(1) parser generator that, when applied to grammar G, produces an LL(1) parser for G if such a parser exists. We use the Coq Proof Assistant to verify that the generator and the parsers that it produces are sound and complete, and that they terminate on all inputs without using fuel parameters. As a case study, we extract the tool’s source code and use it to generate a JSON parser. The generated parser runs in linear time; it is two to four times slower than an unverified parser for the same grammar.

Cite as

Sam Lasser, Chris Casinghino, Kathleen Fisher, and Cody Roux. A Verified LL(1) Parser Generator. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{lasser_et_al:LIPIcs.ITP.2019.24,
  author =	{Lasser, Sam and Casinghino, Chris and Fisher, Kathleen and Roux, Cody},
  title =	{{A Verified LL(1) Parser Generator}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{24:1--24:18},
  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.2019.24},
  URN =		{urn:nbn:de:0030-drops-110794},
  doi =		{10.4230/LIPIcs.ITP.2019.24},
  annote =	{Keywords: interactive theorem proving, top-down parsing}
}
Document
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}
}
Document
Life Is Random, Time Is Not: Markov Decision Processes with Window Objectives

Authors: Thomas Brihaye, Florent Delgrange, Youssouf Oualhadj, and Mickael Randour

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


Abstract
The window mechanism was introduced by Chatterjee et al. [Krishnendu Chatterjee et al., 2015] to strengthen classical game objectives with time bounds. It permits to synthesize system controllers that exhibit acceptable behaviors within a configurable time frame, all along their infinite execution, in contrast to the traditional objectives that only require correctness of behaviors in the limit. The window concept has proved its interest in a variety of two-player zero-sum games, thanks to the ability to reason about such time bounds in system specifications, but also the increased tractability that it usually yields. In this work, we extend the window framework to stochastic environments by considering the fundamental threshold probability problem in Markov decision processes for window objectives. That is, given such an objective, we want to synthesize strategies that guarantee satisfying runs with a given probability. We solve this problem for the usual variants of window objectives, where either the time frame is set as a parameter, or we ask if such a time frame exists. We develop a generic approach for window-based objectives and instantiate it for the classical mean-payoff and parity objectives, already considered in games. Our work paves the way to a wide use of the window mechanism in stochastic models.

Cite as

Thomas Brihaye, Florent Delgrange, Youssouf Oualhadj, and Mickael Randour. Life Is Random, Time Is Not: Markov Decision Processes with Window Objectives. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{brihaye_et_al:LIPIcs.CONCUR.2019.8,
  author =	{Brihaye, Thomas and Delgrange, Florent and Oualhadj, Youssouf and Randour, Mickael},
  title =	{{Life Is Random, Time Is Not: Markov Decision Processes with Window Objectives}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{8:1--8:18},
  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.2019.8},
  URN =		{urn:nbn:de:0030-drops-109103},
  doi =		{10.4230/LIPIcs.CONCUR.2019.8},
  annote =	{Keywords: Markov decision processes, window mean-payoff, window parity}
}
Document
A Theory AB Toolbox

Authors: Marco Gaboardi and Justin Hsu

Published in: LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)


Abstract
Randomized algorithms are a staple of the theoretical computer science literature. By careful use of randomness, algorithms can achieve properties that are simply not possible with deterministic algorithms. Today, these properties are proved on paper, by theoretical computer scientists; we investigate formally verifying these proofs. The main challenges are two: proofs about algorithms can be quite complex, using various facts from probability theory; and proofs are highly customized - two proofs of the same property for two algorithms can be completely different. To overcome these challenges, we propose taking inspiration from paper proofs, by building common tools - abstractions, reasoning principles, perhaps even notations - into a formal verification toolbox. To give an idea of our approach, we consider three common patterns in paper proofs: the union bound, concentration bounds, and martingale arguments.

Cite as

Marco Gaboardi and Justin Hsu. A Theory AB Toolbox. In 1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. 129-139, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{gaboardi_et_al:LIPIcs.SNAPL.2015.129,
  author =	{Gaboardi, Marco and Hsu, Justin},
  title =	{{A Theory AB Toolbox}},
  booktitle =	{1st Summit on Advances in Programming Languages (SNAPL 2015)},
  pages =	{129--139},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-80-4},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{32},
  editor =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.129},
  URN =		{urn:nbn:de:0030-drops-50225},
  doi =		{10.4230/LIPIcs.SNAPL.2015.129},
  annote =	{Keywords: Verification, randomized algorithms}
}
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