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Documents authored by Gadducci, Fabio

Document
DOI: 10.4230/LIPIcs.CALCO.2023.16
Weakly Markov Categories and Weakly Affine Monads

Authors: Tobias Fritz, Fabio Gadducci, Paolo Perrone, and Davide Trotta

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

Abstract
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the structure of a commutative comonoid. They arise for example as Kleisli categories of commutative monads on cartesian categories, and as such they provide a general framework for effectful computation. Recently proposed in the context of categorical probability, Markov categories are gs-monoidal categories where the monoidal unit is also terminal, and they arise for example as Kleisli categories of commutative affine monads, where affine means that the monad preserves the monoidal unit. The aim of this paper is to study a new condition on the gs-monoidal structure, resulting in the concept of weakly Markov categories, which is intermediate between gs-monoidal categories and Markov ones. In a weakly Markov category, the morphisms to the monoidal unit are not necessarily unique, but form a group. As we show, these categories exhibit a rich theory of conditional independence for morphisms, generalising the known theory for Markov categories. We also introduce the corresponding notion for commutative monads, which we call weakly affine, and for which we give two equivalent characterisations. The paper argues that these monads are relevant to the study of categorical probability. A case at hand is the monad of finite non-zero measures, which is weakly affine but not affine. Such structures allow to investigate probability without normalisation within an elegant categorical framework.
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Tobias Fritz, Fabio Gadducci, Paolo Perrone, and Davide Trotta. Weakly Markov Categories and Weakly Affine Monads. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fritz_et_al:LIPIcs.CALCO.2023.16,
  author =	{Fritz, Tobias and Gadducci, Fabio and Perrone, Paolo and Trotta, Davide},
  title =	{{Weakly Markov Categories and Weakly Affine Monads}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{16:1--16:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.16},
  URN =		{urn:nbn:de:0030-drops-188133},
  doi =		{10.4230/LIPIcs.CALCO.2023.16},
  annote =	{Keywords: String diagrams, gs-monoidal and Markov categories, categorical probability, affine monads}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.CALCO.2021
LIPIcs, Volume 211, CALCO 2021, Complete Volume

Authors: Fabio Gadducci and Alexandra Silva

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
LIPIcs, Volume 211, CALCO 2021, Complete Volume
Cite as

9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 1-384, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{gadducci_et_al:LIPIcs.CALCO.2021,
  title =	{{LIPIcs, Volume 211, CALCO 2021, Complete Volume}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{1--384},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021},
  URN =		{urn:nbn:de:0030-drops-153544},
  doi =		{10.4230/LIPIcs.CALCO.2021},
  annote =	{Keywords: LIPIcs, Volume 211, CALCO 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.CALCO.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Fabio Gadducci and Alexandra Silva

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gadducci_et_al:LIPIcs.CALCO.2021.0,
  author =	{Gadducci, Fabio and Silva, Alexandra},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{0:i--0:x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.0},
  URN =		{urn:nbn:de:0030-drops-153559},
  doi =		{10.4230/LIPIcs.CALCO.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.42
A Categorical Account of Replicated Data Types

Authors: Fabio Gadducci, Hernán Melgratti, Christian Roldán, and Matteo Sammartino

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Abstract
Replicated Data Types (RDTs) have been introduced as a suitable abstraction for dealing with weakly consistent data stores, which may (temporarily) expose multiple, inconsistent views of their state. In the literature, RDTs are commonly specified in terms of two relations: visibility, which accounts for the different views that a store may have, and arbitration, which states the logical order imposed on the operations executed over the store. Different flavours, e.g., operational, axiomatic and functional, have recently been proposed for the specification of RDTs. In this work, we propose an algebraic characterisation of RDT specifications. We define categories of visibility relations and arbitrations, show the existence of relevant limits and colimits, and characterize RDT specifications as functors between such categories that preserve these additional structures.
Cite as

Fabio Gadducci, Hernán Melgratti, Christian Roldán, and Matteo Sammartino. A Categorical Account of Replicated Data Types. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 42:1-42:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{gadducci_et_al:LIPIcs.FSTTCS.2019.42,
  author =	{Gadducci, Fabio and Melgratti, Hern\'{a}n and Rold\'{a}n, Christian and Sammartino, Matteo},
  title =	{{A Categorical Account of Replicated Data Types}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{42:1--42:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.42},
  URN =		{urn:nbn:de:0030-drops-116042},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.42},
  annote =	{Keywords: Replicated data type, Specification, Functorial characterisation}
}
Document
DOI: 10.4230/DagRep.5.11.1
Verification of Evolving Graph Structures (Dagstuhl Seminar 15451)

Authors: Parosh Aziz Abdulla, Fabio Gadducci, Barbara König, and Viktor Vafeiadis

Published in: Dagstuhl Reports, Volume 5, Issue 11 (2016)

Abstract
This report documents the programme and the outcome of Dagstuhl Seminar 15451 "Verification of Evolving Graph Structures". The aim was to bring together researchers from different communities (shape analysis, separation logic, graph transformation, verification of infinite-state systems) who are interested in developing techniques for the analysis of graph manipulations, i.e., methods that are able to handle the challenges that arise in current verification problems. Apart from scientific talks, the programme also included four tutorial talks and four working groups, which are summarized in this report.
Cite as

Parosh Aziz Abdulla, Fabio Gadducci, Barbara König, and Viktor Vafeiadis. Verification of Evolving Graph Structures (Dagstuhl Seminar 15451). In Dagstuhl Reports, Volume 5, Issue 11, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Article{azizabdulla_et_al:DagRep.5.11.1,
  author =	{Aziz Abdulla, Parosh and Gadducci, Fabio and K\"{o}nig, Barbara and Vafeiadis, Viktor},
  title =	{{Verification of Evolving Graph Structures (Dagstuhl Seminar 15451)}},
  pages =	{1--28},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{5},
  number =	{11},
  editor =	{Aziz Abdulla, Parosh and Gadducci, Fabio and K\"{o}nig, Barbara and Vafeiadis, Viktor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.5.11.1},
  URN =		{urn:nbn:de:0030-drops-57614},
  doi =		{10.4230/DagRep.5.11.1},
  annote =	{Keywords: dynamic systems, graph transformation, graphs, heap analysis, separation logic, shape analysis, static analysis, verification}
}
Document
DOI: 10.4230/DagRep.4.4.49
Categorical Methods at the Crossroads (Dagstuhl Perspectives Workshop 14182)

Authors: Samson Abramsky, John C. Baez, Fabio Gadducci, and Viktor Winschel

Published in: Dagstuhl Reports, Volume 4, Issue 4 (2014)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 14182 "Perspectives Workshop: Categorical Methods at the Crossroads". The aim of the meeting was to investigate the potential of category theory as a paradigm for mathematical modeling and applied science. The envisaged application areas included computation, physics, biology, complex systems, social and cognitive science and linguistics. Many of these areas were indeed tackled in the variety of topics dealt with during the workshop. Each working day followed the same structure: two survey lectures during the morning, followed by two/three shorter talks in the afternoon, and closed by a working group session. During these sessions the attendants split into several groups according to the main thematic areas that had been identified on the first day. Both surveys and talks are reported in the "Overview" section of the report, while a wrap-up of the discussions that occurred inside the working groups is reported in the "Working Groups" section.
Cite as

Samson Abramsky, John C. Baez, Fabio Gadducci, and Viktor Winschel. Categorical Methods at the Crossroads (Dagstuhl Perspectives Workshop 14182). In Dagstuhl Reports, Volume 4, Issue 4, pp. 49-63, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Article{abramsky_et_al:DagRep.4.4.49,
  author =	{Abramsky, Samson and Baez, John C. and Gadducci, Fabio and Winschel, Viktor},
  title =	{{Categorical Methods at the Crossroads (Dagstuhl Perspectives Workshop 14182)}},
  pages =	{49--63},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2014},
  volume =	{4},
  number =	{4},
  editor =	{Abramsky, Samson and Baez, John C. and Gadducci, Fabio and Winschel, Viktor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.4.4.49},
  URN =		{urn:nbn:de:0030-drops-46189},
  doi =		{10.4230/DagRep.4.4.49},
  annote =	{Keywords: Category theory, concurrency, economics, game theory, logics, quantum computing, semantics}
}
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