8 Search Results for "Seiller, Thomas"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.16
The Agafonov and Schnorr-Stimm Theorems for Probabilistic Automata

Authors: Laurent Bienvenu, Hugo Gimbert, and Subin Pulari

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
For a fixed alphabet A, an infinite sequence X is said to be normal if every word w over A appears in X with the same frequency as any other word of the same length. A classical result of Agafonov (1966) relates normality to finite automata as follows: a sequence X is normal if and only if any subsequence of X selected by a finite automaton is itself normal. Another theorem of Schnorr and Stimm (1972) gives an alternative characterization: a sequence X is normal if and only if no gambler can win large amounts of money by betting on the sequence X using a strategy that can be described by a finite automaton. Both of these theorems are established in the setting of deterministic finite automata. This raises the question as to whether they can be extended to the setting of probabilistic finite automata. In the case of the Agafonov theorem, a partial positive answer was given by Léchine et al. (MFCS 2024) in a restricted case of probabilistic automata with rational transition probabilities. In this paper, we settle the full conjecture by proving that both the Agafonov and the Schnorr-Stimm theorems hold true for arbitrary probabilistic automata. Specifically, we show that a sequence X is normal if and only if any probabilistic automaton selects a normal subsequence of X with probability 1 and also show that a sequence X is normal if and only if any probabilistic finite-state gambler fails to win on X with probability 1.
Cite as

Laurent Bienvenu, Hugo Gimbert, and Subin Pulari. The Agafonov and Schnorr-Stimm Theorems for Probabilistic Automata. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bienvenu_et_al:LIPIcs.FSTTCS.2025.16,
  author =	{Bienvenu, Laurent and Gimbert, Hugo and Pulari, Subin},
  title =	{{The Agafonov and Schnorr-Stimm Theorems for Probabilistic Automata}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.16},
  URN =		{urn:nbn:de:0030-drops-250978},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.16},
  annote =	{Keywords: Normality, Agafonov theorem, probabilistic automata}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.23
∞-Categorical Models of Linear Logic

Authors: Eliès Harington and Samuel Mimram

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

Abstract
The notion of categorical model of linear logic is now well studied and established around the notion of linear-non-linear adjunction, which encompasses the earlier notions of Seely categories, Lafont categories and linear categories. These categorical structures have counterparts in the realm of ∞-categories, which can thus be thought of as weak forms of models of linear logic. The goal of this article is to formally introduce them and study their relationships. We show that ∞-linear-non-linear adjunctions still play the role of a unifying notion of model in this setting. Moreover, we provide a sufficient condition for a symmetric monoidal ∞-category to be Lafont. Finally, we illustrate our constructions by providing models: we construct linear-non-linear adjunctions that generalize well-known models in relations (and variants based on profunctors or spans), domains and vector spaces. In particular, we introduce a model based on spectra, a homotopical variant of abelian groups.
Cite as

Eliès Harington and Samuel Mimram. ∞-Categorical Models of Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harington_et_al:LIPIcs.FSCD.2025.23,
  author =	{Harington, Eli\`{e}s and Mimram, Samuel},
  title =	{{∞-Categorical Models of Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.23},
  URN =		{urn:nbn:de:0030-drops-236381},
  doi =		{10.4230/LIPIcs.FSCD.2025.23},
  annote =	{Keywords: linear logic, linear-non-linear adjunction, ∞-category, spectrum}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.43
Linear Realisability over Nets: Multiplicatives

Authors: Adrien Ragot, Thomas Seiller, and Lorenzo Tortora de Falco

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We provide a new realisability model based on orthogonality for the multiplicative fragment of linear logic, both in presence of generalised axioms (MLL^✠) and in the standard case (MLL). The novelty is the definition of cut elimination for generalised axioms. We prove that our model is adequate and complete both for MLL^✠ and MLL.
Cite as

Adrien Ragot, Thomas Seiller, and Lorenzo Tortora de Falco. Linear Realisability over Nets: Multiplicatives. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 43:1-43:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ragot_et_al:LIPIcs.CSL.2025.43,
  author =	{Ragot, Adrien and Seiller, Thomas and Tortora de Falco, Lorenzo},
  title =	{{Linear Realisability over Nets: Multiplicatives}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{43:1--43:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.43},
  URN =		{urn:nbn:de:0030-drops-228002},
  doi =		{10.4230/LIPIcs.CSL.2025.43},
  annote =	{Keywords: Linear Logic, Proof Nets, Realisability, Orthogonality, Hypergraphs, Rewriting, Correctness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.67
Agafonov’s Theorem for Probabilistic Selectors

Authors: Ulysse Léchine, Thomas Seiller, and Jakob Grue Simonsen

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
A normal sequence over {0,1} is an infinite sequence for which every word of length k appears with frequency 2^{-k}. Agafonov’s eponymous theorem states that selection by a finite state selector preserves normality, i.e. if α is a normal sequence and A is a finite state selector, then the subsequence A(α) is either finite or a normal sequence. In this work, we address the following question: does this result hold when considering probabilistic selectors? We provide a partial positive answer, in the case where the probabilities involved are rational. More formally, we prove that given a normal sequence α and a rational probabilistic selector P, the selected subsequence P(α) will be a normal sequence with probability 1.
Cite as

Ulysse Léchine, Thomas Seiller, and Jakob Grue Simonsen. Agafonov’s Theorem for Probabilistic Selectors. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 67:1-67:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lechine_et_al:LIPIcs.MFCS.2024.67,
  author =	{L\'{e}chine, Ulysse and Seiller, Thomas and Simonsen, Jakob Grue},
  title =	{{Agafonov’s Theorem for Probabilistic Selectors}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{67:1--67:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.67},
  URN =		{urn:nbn:de:0030-drops-206238},
  doi =		{10.4230/LIPIcs.MFCS.2024.67},
  annote =	{Keywords: Normal sequences, probabilistic automata, Agafonov’s theorem}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.26
mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity

Authors: Clément Aubert, Thomas Rubiano, Neea Rusch, and Thomas Seiller

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

Abstract
Implicit Computational Complexity (ICC) drives better understanding of complexity classes, but it also guides the development of resources-aware languages and static source code analyzers. Among the methods developed, the mwp-flow analysis [Jones and Lars Kristiansen, 2009] certifies polynomial bounds on the size of the values manipulated by an imperative program. This result is obtained by bounding the transitions between states instead of focusing on states in isolation, as most static analyzers do, and is not concerned with termination or tight bounds on values. Those differences, along with its built-in compositionality, make the mwp-flow analysis a good target for determining how ICC-inspired techniques diverge compared with more traditional static analysis methods. This paper’s contributions are three-fold: we fine-tune the internal machinery of the original analysis to make it tractable in practice; we extend the analysis to function calls and leverage its machinery to compute the result of the analysis efficiently; and we implement the resulting analysis as a lightweight tool to automatically perform data-size analysis of C programs. This documented effort prepares and enables the development of certified complexity analysis, by transforming a costly analysis into a tractable program, that furthermore decorrelates the problem of deciding if a bound exist with the problem of computing it.
Cite as

Clément Aubert, Thomas Rubiano, Neea Rusch, and Thomas Seiller. mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 26:1-26:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{aubert_et_al:LIPIcs.FSCD.2022.26,
  author =	{Aubert, Cl\'{e}ment and Rubiano, Thomas and Rusch, Neea and Seiller, Thomas},
  title =	{{mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{26:1--26:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.26},
  URN =		{urn:nbn:de:0030-drops-163071},
  doi =		{10.4230/LIPIcs.FSCD.2022.26},
  annote =	{Keywords: Static Program Analysis, Implicit Computational Complexity, Automatic Complexity Analysis, Program Verification}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.135
Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic

Authors: Lê Thành Dũng Nguyễn and Cécilia Pradic

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We give a characterization of star-free languages in a λ-calculus with support for non-commutative affine types (in the sense of linear logic), via the algebraic characterization of the former using aperiodic monoids. When the type system is made commutative, we show that we get regular languages instead. A key ingredient in our approach – that it shares with higher-order model checking – is the use of Church encodings for inputs and outputs. Our result is, to our knowledge, the first use of non-commutativity in implicit computational complexity.
Cite as

Lê Thành Dũng Nguyễn and Cécilia Pradic. Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 135:1-135:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{nguyen_et_al:LIPIcs.ICALP.2020.135,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, C\'{e}cilia},
  title =	{{Implicit Automata in Typed \lambda-Calculi I: Aperiodicity in a Non-Commutative Logic}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{135:1--135:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.135},
  URN =		{urn:nbn:de:0030-drops-125426},
  doi =		{10.4230/LIPIcs.ICALP.2020.135},
  annote =	{Keywords: Church encodings, ordered linear types, star-free languages}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.123
From Normal Functors to Logarithmic Space Queries (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Lê Thành Dũng Nguyễn and Cécilia Pradic

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We introduce a new approach to implicit complexity in linear logic, inspired by functional database query languages and using recent developments in effective denotational semantics of polymorphism. We give the first sub-polynomial upper bound in a type system with impredicative polymorphism; adding restrictions on quantifiers yields a characterization of logarithmic space, for which extensional completeness is established via descriptive complexity.
Cite as

Lê Thành Dũng Nguyễn and Cécilia Pradic. From Normal Functors to Logarithmic Space Queries (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 123:1-123:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{nguyen_et_al:LIPIcs.ICALP.2019.123,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, C\'{e}cilia},
  title =	{{From Normal Functors to Logarithmic Space Queries}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{123:1--123:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.123},
  URN =		{urn:nbn:de:0030-drops-106994},
  doi =		{10.4230/LIPIcs.ICALP.2019.123},
  annote =	{Keywords: coherence spaces, elementary linear logic, semantic evaluation}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.86
An Intensionally Fully-abstract Sheaf Model for pi

Authors: Clovis Eberhart, Tom Hirschowitz, and Thomas Seiller

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
Following previous work on CCS, we propose a compositional model for the pi-calculus in which processes are interpreted as sheaves on certain simple sites. We define an analogue of fair testing equivalence in the model and show that our interpretation is intensionally fully abstract for it. That is, the interpretation preserves and reflects fair testing equivalence; and furthermore, any strategy is fair testing equivalent to the interpretation of some process. The central part of our work is the construction of our sites, whose heart is a combinatorial presentation of pi-calculus traces in the spirit of string diagrams. As in previous work, the sheaf condition is analogous to innocence in Hyland-Ong/Nickau games.
Cite as

Clovis Eberhart, Tom Hirschowitz, and Thomas Seiller. An Intensionally Fully-abstract Sheaf Model for pi. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 86-100, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{eberhart_et_al:LIPIcs.CALCO.2015.86,
  author =	{Eberhart, Clovis and Hirschowitz, Tom and Seiller, Thomas},
  title =	{{An Intensionally Fully-abstract Sheaf Model for pi}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{86--100},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.86},
  URN =		{urn:nbn:de:0030-drops-55284},
  doi =		{10.4230/LIPIcs.CALCO.2015.86},
  annote =	{Keywords: concurrency, sheaves, causal models, games}
}
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