8 Search Results for "Doyen, Laurent"

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.CONCUR.2024.23
Regular Games with Imperfect Information Are Not That Regular

Authors: Laurent Doyen and Thomas Soullard

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other player. Imperfect information is modeled by an indistinguishability relation describing the pairs of histories that the first player cannot distinguish, a generalization of the traditional model with partial observations. The game is regular if it admits a regular function whose kernel commutes with the indistinguishability relation. The synthesis of pure strategies that ensure all possible outcomes satisfy the objective is possible in regular games, by a generic reduction that holds for all objectives. While the solution for pure strategies extends to randomized strategies in the traditional model with partial observations (which is always regular), a similar reduction does not exist in the more general model. Despite that, we show that in regular games with Büchi objectives the synthesis problem is decidable for randomized strategies that ensure the outcome satisfies the objective almost-surely.
Cite as

Laurent Doyen and Thomas Soullard. Regular Games with Imperfect Information Are Not That Regular. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doyen_et_al:LIPIcs.CONCUR.2024.23,
  author =	{Doyen, Laurent and Soullard, Thomas},
  title =	{{Regular Games with Imperfect Information Are Not That Regular}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.23},
  URN =		{urn:nbn:de:0030-drops-207953},
  doi =		{10.4230/LIPIcs.CONCUR.2024.23},
  annote =	{Keywords: Imperfect-information games, randomized strategies, synthesis}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.15
Antichain with SAT and Tries

Authors: Lukáš Holík and Pavol Vargovčík

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
We introduce a SAT-enabled version of an antichain algorithm for checking language emptiness of alternating finite automata (AFA) with complex transition relations encoded as compact logical formulae. The SAT solver is used to compute predecessors of AFA configurations, and at the same time, to evaluate the subsumption of newly found configurations in the antichain of the previously found ones. The algorithm could be naively implemented by an incremental SAT solver where the growing antichain is represented by adding new clauses. To make it efficient, we 1) force the SAT solver to prioritize largest/subsumption-strongest predecessors (so that weaker configurations are not even generated), and 2) store the antichain clauses in a special variant of a trie that allows fast subsumption testing. The experimental results suggest that the resulting emptiness checker is very efficient compared to the state of the art and that our techniques improve the performance of the SAT solver.
Cite as

Lukáš Holík and Pavol Vargovčík. Antichain with SAT and Tries. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 15:1-15:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{holik_et_al:LIPIcs.SAT.2024.15,
  author =	{Hol{\'\i}k, Luk\'{a}\v{s} and Vargov\v{c}{\'\i}k, Pavol},
  title =	{{Antichain with SAT and Tries}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{15:1--15:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.15},
  URN =		{urn:nbn:de:0030-drops-205372},
  doi =		{10.4230/LIPIcs.SAT.2024.15},
  annote =	{Keywords: SAT, Trie, Antichain, Alternating automata, Subset query}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.48
Observation and Distinction. Representing Information in Infinite Games

Authors: Dietmar Berwanger and Laurent Doyen

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
We compare two approaches for modelling imperfect information in infinite games by using finite-state automata. The first, more standard approach views information as the result of an observation process driven by a sequential Mealy machine. In contrast, the second approach features indistinguishability relations described by synchronous two-tape automata. The indistinguishability-relation model turns out to be strictly more expressive than the one based on observations. We present a characterisation of the indistinguishability relations that admit a representation as a finite-state observation function. We show that the characterisation is decidable, and give a procedure to construct a corresponding Mealy machine whenever one exists.
Cite as

Dietmar Berwanger and Laurent Doyen. Observation and Distinction. Representing Information in Infinite Games. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{berwanger_et_al:LIPIcs.STACS.2020.48,
  author =	{Berwanger, Dietmar and Doyen, Laurent},
  title =	{{Observation and Distinction. Representing Information in Infinite Games}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{48:1--48:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.48},
  URN =		{urn:nbn:de:0030-drops-119095},
  doi =		{10.4230/LIPIcs.STACS.2020.48},
  annote =	{Keywords: Infinite Games on Finite Graphs, Imperfect Information, Automatic Structures}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.98
Computation Tree Logic for Synchronization Properties

Authors: Krishnendu Chatterjee and Laurent Doyen

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We present a logic that extends CTL (Computation Tree Logic) with operators that express synchronization properties. A property is synchronized in a system if it holds in all paths of a certain length. The new logic is obtained by using the same path quantifiers and temporal operators as in CTL, but allowing a different order of the quantifiers. This small syntactic variation induces a logic that can express non-regular properties for which known extensions of MSO with equality of path length are undecidable. We show that our variant of CTL is decidable and that the model-checking problem is in Delta_3^P = P^{NP^{NP}}, and is hard for the class of problems solvable in polynomial time using a parallel access to an NP oracle. We analogously consider quantifier exchange in extensions of CTL, and we present operators defined using basic operators of CTL* that express the occurrence of infinitely many synchronization points. We show that the model-checking problem remains in Delta_3^P. The distinguishing power of CTL and of our new logic coincide if the Next operator is allowed in the logics, thus the classical bisimulation quotient can be used for state-space reduction before model checking.
Cite as

Krishnendu Chatterjee and Laurent Doyen. Computation Tree Logic for Synchronization Properties. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 98:1-98:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chatterjee_et_al:LIPIcs.ICALP.2016.98,
  author =	{Chatterjee, Krishnendu and Doyen, Laurent},
  title =	{{Computation Tree Logic for Synchronization Properties}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{98:1--98:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.98},
  URN =		{urn:nbn:de:0030-drops-62334},
  doi =		{10.4230/LIPIcs.ICALP.2016.98},
  annote =	{Keywords: Computation Tree Logic, Synchronization, model-checking, complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.121
Synchronizing Words for Weighted and Timed Automata

Authors: Laurent Doyen, Line Juhl, Kim G. Larsen, Nicolas Markey, and Mahsa Shirmohammadi

Published in: LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

Abstract
The problem of synchronizing automata is concerned with the existence of a word that sends all states of the automaton to one and the same state. This problem has classically been studied for complete deterministic finite automata, with the existence problem being NLOGSPACE-complete. In this paper we consider synchronizing-word problems for weighted and timed automata. We consider the synchronization problem in several variants and combinations of these, including deterministic and non-deterministic timed and weighted automata, synchronization to unique location with possibly different clock valuations or accumulated weights, as well as synchronization with a safety condition forbidding the automaton to visit states outside a safety-set during synchronization (e.g. energy constraints). For deterministic weighted automata, the synchronization problem is proven PSPACE-complete under energy constraints, and in 3-EXPSPACE under general safety constraints. For timed automata the synchronization problems are shown to be PSPACE-complete in the deterministic case, and undecidable in the non-deterministic case.
Cite as

Laurent Doyen, Line Juhl, Kim G. Larsen, Nicolas Markey, and Mahsa Shirmohammadi. Synchronizing Words for Weighted and Timed Automata. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 121-132, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{doyen_et_al:LIPIcs.FSTTCS.2014.121,
  author =	{Doyen, Laurent and Juhl, Line and Larsen, Kim G. and Markey, Nicolas and Shirmohammadi, Mahsa},
  title =	{{Synchronizing Words for Weighted and Timed Automata}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{121--132},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Raman, Venkatesh and Suresh, S. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.121},
  URN =		{urn:nbn:de:0030-drops-48370},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.121},
  annote =	{Keywords: Synchronizing words, weighted automata, timed automata}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2010.505
Generalized Mean-payoff and Energy Games

Authors: Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger, and Jean-François Raskin

Published in: LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

Abstract
In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources. We prove the finite-memory determinacy of generalized energy games and show the inter-reducibility of generalized mean-payoff and energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding the existence of a winning strategy for the protagonist is NP-complete.
Cite as

Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger, and Jean-François Raskin. Generalized Mean-payoff and Energy Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 505-516, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chatterjee_et_al:LIPIcs.FSTTCS.2010.505,
  author =	{Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A. and Raskin, Jean-Fran\c{c}ois},
  title =	{{Generalized Mean-payoff and Energy Games}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{505--516},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Lodaya, Kamal and Mahajan, Meena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.505},
  URN =		{urn:nbn:de:0030-drops-28484},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.505},
  annote =	{Keywords: mean-payoff games, energy games, finite memory strategies, determinacy}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2008.1742
On the Power of Imperfect Information

Authors: Dietmar Berwanger and Laurent Doyen

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

Abstract
We present a polynomial-time reduction from parity games with imperfect information to safety games with imperfect information. Similar reductions for games with perfect information typically increase the game size exponentially. Our construction avoids such a blow-up by using imperfect information to realise succinct counters which cover a range exponentially larger than their size. In particular, the reduction shows that the problem of solving imperfect-information games with safety conditions is \EXPTIME-complete.
Cite as

Dietmar Berwanger and Laurent Doyen. On the Power of Imperfect Information. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 73-82, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{berwanger_et_al:LIPIcs.FSTTCS.2008.1742,
  author =	{Berwanger, Dietmar and Doyen, Laurent},
  title =	{{On the Power of Imperfect Information}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{73--82},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1742},
  URN =		{urn:nbn:de:0030-drops-17427},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1742},
  annote =	{Keywords: Infinite games, imperfect information}
}
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