14 Search Results for "Staton, Sam"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.61
Quantum Relaxations of CSP and Structure Isomorphism

Authors: Amin Karamlou

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We investigate quantum relaxations of two key decision problems in computer science: the constraint satisfaction problem (CSP) and the structure isomorphism problem. CSP asks whether a homomorphism exists between two relational structures, while structure isomorphism seeks an isomorphism between them. In recent years, it has become increasingly apparent that many special cases of CSP can be reformulated in terms of the existence of perfect classical strategies in non-local games, a key topic of study in quantum information theory. These games have allowed us to study quantum advantage in relation to many important decision problems, such as the k-colouring problem, and the problem of solving binary constraint systems. Abramsky et al. (2017) have shown that all of these games can be seen as special instances of a non-local CSP game. Moreover, they show that perfect quantum strategies in this CSP game can be viewed as Kleisli morphisms of a graded monad on the category of relational structures, which they dub the quantum monad. In this way, the quantum monad provides a categorical characterisation of quantum advantage for the non-local CSP game. In this work we solidify and expand the results of Abramsky et al., answering several of their open questions. Firstly, we compare the definition of quantum graph homomorphisms arising from this work with an earlier definition of the concept due to Mančinska and Roberson and show that there are graphs which exhibit quantum advantage under one definition but not the other. Our second contribution is to extend the results of Abramsky et al. which only hold in the tensor product framework of quantum mechanics to the commuting operator framework. Next, we study a non-local structure isomorphism game, which generalises the well-studied graph isomorphism game. We show how the construction of the quantum monad can be refined to provide categorical semantics for quantum strategies in this game. This results in a category where morphisms coincide with quantum homomorphisms and isomorphisms coincide with quantum isomorphisms.
Cite as

Amin Karamlou. Quantum Relaxations of CSP and Structure Isomorphism. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 61:1-61:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{karamlou:LIPIcs.MFCS.2025.61,
  author =	{Karamlou, Amin},
  title =	{{Quantum Relaxations of CSP and Structure Isomorphism}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{61:1--61:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.61},
  URN =		{urn:nbn:de:0030-drops-241686},
  doi =		{10.4230/LIPIcs.MFCS.2025.61},
  annote =	{Keywords: CSP, graph isomorphism, quantum information, non-local game, quantum graph homomorphism, monad}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.23
First-Order Store and Visibility in Name-Passing Calculi

Authors: Daniel Hirschkoff, Iwan Quémerais, and Davide Sangiorgi

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
The π-calculus is the paradigmatical name-passing calculus. While being purely name-passing, it allows the representation of higher-order functions and store. We study how π-calculus processes can be controlled so that computations can only involve storage of first-order values. The discipline is enforced by a type system that is based on the notion of visibility, coming from game semantics. We discuss the impact of visibility on the behavioural theory. We propose characterisations of may-testing and barbed equivalence, based on (variants of) trace equivalence and labelled bisimilarity, in the case where computation is sequential, and in the case where computation is well-bracketed.
Cite as

Daniel Hirschkoff, Iwan Quémerais, and Davide Sangiorgi. First-Order Store and Visibility in Name-Passing Calculi. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirschkoff_et_al:LIPIcs.CONCUR.2025.23,
  author =	{Hirschkoff, Daniel and Qu\'{e}merais, Iwan and Sangiorgi, Davide},
  title =	{{First-Order Store and Visibility in Name-Passing Calculi}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.23},
  URN =		{urn:nbn:de:0030-drops-239737},
  doi =		{10.4230/LIPIcs.CONCUR.2025.23},
  annote =	{Keywords: process calculi, behavioural equivalence, type system}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.12
Cancellative Convex Semilattices

Authors: Ana Sokolova and Harald Woracek

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
Convex semilattices are algebras that are at the same time a convex algebra and a semilattice, together with a distributivity axiom. These algebras have attracted some attention in the last years as suitable algebras for probability and nondeterminism, in particular by being the Eilenberg-Moore algebras of the nonempty finitely-generated convex subsets of the distributions monad. A convex semilattice is cancellative if the underlying convex algebra is cancellative. Cancellative convex algebras have been characterized by M. H. Stone and by H. Kneser: A convex algebra is cancellative if and only if it is isomorphic to a convex subset of a vector space (with canonical convex algebra operations). We prove an analogous theorem for convex semilattices: A convex semilattice is cancellative if and only if it is isomorphic to a convex subset of a Riesz space, i.e., a lattice-ordered vector space (with canonical convex semilattice operations).
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Ana Sokolova and Harald Woracek. Cancellative Convex Semilattices. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sokolova_et_al:LIPIcs.CALCO.2025.12,
  author =	{Sokolova, Ana and Woracek, Harald},
  title =	{{Cancellative Convex Semilattices}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.12},
  URN =		{urn:nbn:de:0030-drops-235714},
  doi =		{10.4230/LIPIcs.CALCO.2025.12},
  annote =	{Keywords: convex semilattice, cancellativity, Riesz space}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CALCO.2025.1
Effectful Mealy Machines: Coalgebraic and Causal Traces (Invited Talk)

Authors: Filippo Bonchi, Elena Di Lavore, and Mario Román

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
We introduce effectful Mealy machines - a general notion of Mealy machine with global effects - and give them semantics in terms of both bisimilarity and traces. Bisimilarity of effectful Mealy machines is characterized syntactically, via free uniform feedback. Their traces are given a novel semantic coinductive universe in terms of effectful streams. We prove that this framework generalizes standard causal processes and captures existing flavours of Mealy machine, bisimilarity, and trace. This is an extended abstract for the manuscript Effectful Mealy Machines: Bisimulation and Trace that will appear in the proceedings of LiCS 2025 [Bonchi et al., 2025]; an extended version with proofs is also available (arxiv.org/abs/2410.10627) [Bonchi et al., 2025]. We additionally characterise causal processes as lax-natural transformations.
Cite as

Filippo Bonchi, Elena Di Lavore, and Mario Román. Effectful Mealy Machines: Coalgebraic and Causal Traces (Invited Talk). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 1:1-1:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2025.1,
  author =	{Bonchi, Filippo and Di Lavore, Elena and Rom\'{a}n, Mario},
  title =	{{Effectful Mealy Machines: Coalgebraic and Causal Traces}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{1:1--1:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.1},
  URN =		{urn:nbn:de:0030-drops-235596},
  doi =		{10.4230/LIPIcs.CALCO.2025.1},
  annote =	{Keywords: Mealy machines, coinduction, copy-discard categories, premonoidal categories}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2024.6
Data Types with Symmetries via Action Containers

Authors: Philipp Joram and Niccolò Veltri

Published in: LIPIcs, Volume 336, 30th International Conference on Types for Proofs and Programs (TYPES 2024)

Abstract
We study two kinds of containers for data types with symmetries in homotopy type theory, and clarify their relationship by introducing the intermediate notion of action containers. Quotient containers are set-valued containers with groups of permissible permutations of positions, interpreted as (possibly non-finitary) analytic functors on the category of sets. Symmetric containers encode symmetries in a groupoid of shapes, and are interpreted accordingly as polynomial functors on the 2-category of groupoids. Action containers are endowed with groups that act on their positions, with morphisms preserving the actions. We show that, as a category, action containers are equivalent to the free coproduct completion of a category of group actions. We derive that they model non-inductive single-variable strictly positive types in the sense of Abbott et al.: The category of action containers is closed under arbitrary (co)products and exponentiation with constants. We equip this category with the structure of a locally groupoidal 2-category, and prove that it locally embeds into the 2-category of symmetric containers. This follows from the embedding of a 2-category of groups into the 2-category of groupoids, extending the delooping construction.
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Philipp Joram and Niccolò Veltri. Data Types with Symmetries via Action Containers. In 30th International Conference on Types for Proofs and Programs (TYPES 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 336, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{joram_et_al:LIPIcs.TYPES.2024.6,
  author =	{Joram, Philipp and Veltri, Niccol\`{o}},
  title =	{{Data Types with Symmetries via Action Containers}},
  booktitle =	{30th International Conference on Types for Proofs and Programs (TYPES 2024)},
  pages =	{6:1--6:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-376-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{336},
  editor =	{M{\o}gelberg, Rasmus Ejlers and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2024.6},
  URN =		{urn:nbn:de:0030-drops-233681},
  doi =		{10.4230/LIPIcs.TYPES.2024.6},
  annote =	{Keywords: Containers, Homotopy Type Theory, Agda, 2-categories}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.30
A Complete Inference System for Probabilistic Infinite Trace Equivalence

Authors: Corina Cîrstea, Lawrence S. Moss, Victoria Noquez, Todd Schmid, Alexandra Silva, and Ana Sokolova

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

Abstract
We present the first sound and complete axiomatization of infinite trace semantics for generative probabilistic transition systems. Our approach is categorical, and we build on recent results on proper functors over convex sets. At the core of our proof is a characterization of infinite traces as the final coalgebra of a functor over convex algebras. Somewhat surprisingly, our axiomatization of infinite trace semantics coincides with that of finite trace semantics, even though the techniques used in the completeness proof are significantly different.
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Corina Cîrstea, Lawrence S. Moss, Victoria Noquez, Todd Schmid, Alexandra Silva, and Ana Sokolova. A Complete Inference System for Probabilistic Infinite Trace Equivalence. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cirstea_et_al:LIPIcs.CSL.2025.30,
  author =	{C\^{i}rstea, Corina and Moss, Lawrence S. and Noquez, Victoria and Schmid, Todd and Silva, Alexandra and Sokolova, Ana},
  title =	{{A Complete Inference System for Probabilistic Infinite Trace Equivalence}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{30:1--30:23},
  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.2025.30},
  URN =		{urn:nbn:de:0030-drops-227870},
  doi =		{10.4230/LIPIcs.CSL.2025.30},
  annote =	{Keywords: Coalgebra, infinite trace, semantics, logic, convex sets}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.14
Two-Dimensional Kripke Semantics I: Presheaves

Authors: G. A. Kavvos

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely through their categorical semantics. We show how the two correspond.
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G. A. Kavvos. Two-Dimensional Kripke Semantics I: Presheaves. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kavvos:LIPIcs.FSCD.2024.14,
  author =	{Kavvos, G. A.},
  title =	{{Two-Dimensional Kripke Semantics I: Presheaves}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.14},
  URN =		{urn:nbn:de:0030-drops-203438},
  doi =		{10.4230/LIPIcs.FSCD.2024.14},
  annote =	{Keywords: modal logic, categorical semantics, Kripke semantics, duality, open maps}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2023.13
A Category for Unifying Gaussian Probability and Nondeterminism

Authors: Dario Stein and Richard Samuelson

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

Abstract
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in statistics, engineering, and control theory, but combining them in a single formalism is challenging. It enables us to rigorously describe a variety of phenomena like noisy physical laws, Willems' theory of open systems and uninformative priors in Bayesian statistics. The core idea is to formally admit vector subspaces D ⊆ X as generalized uniform probability distribution. Our formalism represents a first bridge between the literature on categorical systems theory (signal-flow diagrams, linear relations, hypergraph categories) and notions of probability theory.
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Dario Stein and Richard Samuelson. A Category for Unifying Gaussian Probability and Nondeterminism. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{stein_et_al:LIPIcs.CALCO.2023.13,
  author =	{Stein, Dario and Samuelson, Richard},
  title =	{{A Category for Unifying Gaussian Probability and Nondeterminism}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.13},
  URN =		{urn:nbn:de:0030-drops-188107},
  doi =		{10.4230/LIPIcs.CALCO.2023.13},
  annote =	{Keywords: systems theory, hypergraph categories, Bayesian inference, category theory, Markov categories}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2021.4
Some Formal Structures in Probability (Invited Talk)

Authors: Sam Staton

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
This invited talk will discuss how developments in the Formal Structures for Computation and Deduction can also suggest new directions for the foundations of probability theory. I plan to focus on two aspects: abstraction, and laziness. I plan to highlight two challenges: higher-order random functions, and stochastic memoization.
Cite as

Sam Staton. Some Formal Structures in Probability (Invited Talk). In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 4:1-4:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{staton:LIPIcs.FSCD.2021.4,
  author =	{Staton, Sam},
  title =	{{Some Formal Structures in Probability}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{4:1--4:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.4},
  URN =		{urn:nbn:de:0030-drops-142421},
  doi =		{10.4230/LIPIcs.FSCD.2021.4},
  annote =	{Keywords: Probabilistic programming}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.25
Recursion and Sequentiality in Categories of Sheaves

Authors: Cristina Matache, Sean Moss, and Sam Staton

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
We present a fully abstract model of a call-by-value language with higher-order functions, recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by the fully abstract models of O'Hearn, Riecke and Sandholm, and Marz and Streicher. In contrast with semantics based on cpo’s, we treat recursion as just one feature in a model built by combining a choice of modular components.
Cite as

Cristina Matache, Sean Moss, and Sam Staton. Recursion and Sequentiality in Categories of Sheaves. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{matache_et_al:LIPIcs.FSCD.2021.25,
  author =	{Matache, Cristina and Moss, Sean and Staton, Sam},
  title =	{{Recursion and Sequentiality in Categories of Sheaves}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{25:1--25:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.25},
  URN =		{urn:nbn:de:0030-drops-142631},
  doi =		{10.4230/LIPIcs.FSCD.2021.25},
  annote =	{Keywords: Denotational semantics, Full abstraction, Recursion, Sheaf toposes, CPOs}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2020.16
Infinite Probabilistic Databases

Authors: Martin Grohe and Peter Lindner

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Abstract
Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries.
Cite as

Martin Grohe and Peter Lindner. Infinite Probabilistic Databases. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{grohe_et_al:LIPIcs.ICDT.2020.16,
  author =	{Grohe, Martin and Lindner, Peter},
  title =	{{Infinite Probabilistic Databases}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{16:1--16:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.16},
  URN =		{urn:nbn:de:0030-drops-119400},
  doi =		{10.4230/LIPIcs.ICDT.2020.16},
  annote =	{Keywords: Probabilistic Databases, Possible Worlds Semantics, Query Measurability, Relational Algebra, Aggregate Queries}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.ICALP.2018.3
Probability Theory from a Programming Perspective (Invited Paper)

Authors: Sam Staton

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
A leading idea is to apply techniques from verification and programming theory to machine learning and statistics, to deal with things like compositionality and various notions of correctness and complexity. Probabilistic programming is an example of this. Moreover, this approach leads to new foundational methods in probability theory. This is particularly true in the "non-parametric" aspects, for example in higher-order functions and infinite random graph models.
Cite as

Sam Staton. Probability Theory from a Programming Perspective (Invited Paper). In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{staton:LIPIcs.ICALP.2018.3,
  author =	{Staton, Sam},
  title =	{{Probability Theory from a Programming Perspective}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.3},
  URN =		{urn:nbn:de:0030-drops-90073},
  doi =		{10.4230/LIPIcs.ICALP.2018.3},
  annote =	{Keywords: correctness, complexity, statistics}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.141
The Beta-Bernoulli process and algebraic effects

Authors: Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, and Daniel M. Roy

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
In this paper we use the framework of algebraic effects from programming language theory to analyze the Beta-Bernoulli process, a standard building block in Bayesian models. Our analysis reveals the importance of abstract data types, and two types of program equations, called commutativity and discardability. We develop an equational theory of terms that use the Beta-Bernoulli process, and show that the theory is complete with respect to the measure-theoretic semantics, and also in the syntactic sense of Post. Our analysis has a potential for being generalized to other stochastic processes relevant to Bayesian modelling, yielding new understanding of these processes from the perspective of programming.
Cite as

Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, and Daniel M. Roy. The Beta-Bernoulli process and algebraic effects. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 141:1-141:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{staton_et_al:LIPIcs.ICALP.2018.141,
  author =	{Staton, Sam and Stein, Dario and Yang, Hongseok and Ackerman, Nathanael L. and Freer, Cameron E. and Roy, Daniel M.},
  title =	{{The Beta-Bernoulli process and algebraic effects}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{141:1--141:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.141},
  URN =		{urn:nbn:de:0030-drops-91456},
  doi =		{10.4230/LIPIcs.ICALP.2018.141},
  annote =	{Keywords: Beta-Bernoulli process, Algebraic effects, Probabilistic programming, Exchangeability}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.45
Models for Polymorphism over Physical Dimension

Authors: Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, and Sam Staton

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
We provide a categorical framework for models of a type theory that has special types for physical quantities. The types are indexed by the physical dimensions that they involve. Fibrations are used to organize this index structure in the models of the type theory. We develop some informative models of this type theory: firstly, a model based on group actions, which captures invariance under scaling, and secondly, a way of constructing new models using relational parametricity.
Cite as

Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, and Sam Staton. Models for Polymorphism over Physical Dimension. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 45-59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{atkey_et_al:LIPIcs.TLCA.2015.45,
  author =	{Atkey, Robert and Ghani, Neil and Nordvall Forsberg, Fredrik and Revell, Timothy and Staton, Sam},
  title =	{{Models for Polymorphism over Physical Dimension}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{45--59},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.45},
  URN =		{urn:nbn:de:0030-drops-51547},
  doi =		{10.4230/LIPIcs.TLCA.2015.45},
  annote =	{Keywords: Category Theory, Units of Measure, Dimension Types, Type Theory}
}
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