31 Search Results for "Gadducci, Fabio"

Volume

LIPIcs, Volume 211

9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

CALCO 2021, August 31 to September 3, 2021, Salzburg, Austria

Editors: Fabio Gadducci and Alexandra Silva

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.
Cite as

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.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

Fabio Gadducci and Alexandra Silva. LIPIcs, Volume 211, CALCO 2021, Complete Volume. In 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.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

Fabio Gadducci and Alexandra Silva. Front Matter, Table of Contents, Preface, Conference Organization. In 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.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
Invited Talk
DOI: 10.4230/LIPIcs.CALCO.2021.1
Distributive Laws for Lawvere Theories (Invited Talk)

Authors: Eugenia Cheng

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

Abstract
Distributive laws give a way of combining two algebraic structures expressed as monads; in this work we propose a theory of distributive laws for combining algebraic structures expressed as Lawvere theories. We propose four approaches, involving profunctors, monoidal profunctors, an extension of the free finite-product category 2-monad from Cat to Prof, and factorisation systems respectively. We exhibit comparison functors between CAT and each of these new frameworks to show that the distributive laws between the Lawvere theories correspond in a suitable way to distributive laws between their associated finitary monads. The different but equivalent formulations then provide, between them, a framework conducive to generalisation, but also an explicit description of the composite theories arising from distributive laws.
Cite as

Eugenia Cheng. Distributive Laws for Lawvere Theories (Invited Talk). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, p. 1:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cheng:LIPIcs.CALCO.2021.1,
  author =	{Cheng, Eugenia},
  title =	{{Distributive Laws for Lawvere Theories}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{1:1--1:1},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.1},
  URN =		{urn:nbn:de:0030-drops-153560},
  doi =		{10.4230/LIPIcs.CALCO.2021.1},
  annote =	{Keywords: Distributive laws, Monads, Lawvere theories}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CALCO.2021.2
Towards Engineering Smart Cyber-Physical Systems with Graph Transformation Systems (Invited Talk)

Authors: Holger Giese

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

Abstract
A dramatic transformation of our technical world towards smart cyber-physical systems can be currently observed. This transformation results in a networked technical world where besides the embedded systems with their interaction with the physical world the interconnection of these nodes in the cyber world becomes a key element. Furthermore, there is a strong trend towards smart systems where artificial intelligence techniques and in particular machine learning is employed to make software behave accordingly. This raises the question whether our capabilities to model these future embedded systems are ready to tackle the resulting challenges. In this presentation, we will first discuss how extensions of graph transformation systems can be employed to design and analyse the envisioned future cyber-physical systems with an emphasis on the synergies networking can offer and then characterise which challenges for the design, production, and operation of these systems and how they can be tacked with graph transformation systems. We will therefore discuss to what extent our current capabilities in particular concerning engineering with graph transformation systems match these challenges and where substantial improvements for the graph transformation systems have been crucial and will be crucial in the future. Models are used in classical engineering to plan systems upfront to maximise envisioned properties resp. minimise cost. For smart cyber-physical systems this decoupling of development-time and run-time considerations vanishes, and self-adaptation and runtime models have been advocated as concepts to shift some considerations to run-time. We will review the underlying causes for this shift to run-time, discuss some our work with graph transformation systems in this direction, and outline related open challenges and implications for future work for graph transformation systems to engineer smart cyber-physical systems.
Cite as

Holger Giese. Towards Engineering Smart Cyber-Physical Systems with Graph Transformation Systems (Invited Talk). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, p. 2:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{giese:LIPIcs.CALCO.2021.2,
  author =	{Giese, Holger},
  title =	{{Towards Engineering Smart Cyber-Physical Systems with Graph Transformation Systems}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{2:1--2:1},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.2},
  URN =		{urn:nbn:de:0030-drops-153573},
  doi =		{10.4230/LIPIcs.CALCO.2021.2},
  annote =	{Keywords: Cyber-physical systems, Graph transformation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CALCO.2021.3
Dialectica Comonads (Invited Talk)

Authors: Valeria de Paiva

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

Abstract
Dialectica categories are interesting categorical models of Linear Logic which preserve the differences between linear connectives that the logic is supposed to make, unlike some of the most traditional models like coherence spaces. They arise from the categorical modelling of Gödel’s Dialectica interpretation and seem to be having a revival: connections between Dialectica constructions and containers, lenses and polynomials have been described recently in the literature. In this note I will recap the basic Dialectica constructions and then go on to describe the less well-known interplay of comonads, coalgebras and comonoids that characterizes the composite functor standing for the "of course!" operator in dialectica categories. This composition of comonads evokes some work on stateful games by Laird and others, also discussed in the setting of Reddy’s system LLMS (Linear Logic Model of State).
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Valeria de Paiva. Dialectica Comonads (Invited Talk). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 3:1-3:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{depaiva:LIPIcs.CALCO.2021.3,
  author =	{de Paiva, Valeria},
  title =	{{Dialectica Comonads}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{3:1--3:13},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.3},
  URN =		{urn:nbn:de:0030-drops-153581},
  doi =		{10.4230/LIPIcs.CALCO.2021.3},
  annote =	{Keywords: Dialectica categories, Linear logic, Comonads}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CALCO.2021.4
The Challenges of Weak Persistency (Invited Talk)

Authors: Viktor Vafeiadis

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

Abstract
Non-volatile memory (NVM) is a new hardware technology that provides durable storage at performance similar to that of plain volatile RAM. As such, there is a lot of interest in exploiting this technology to improve the performance of existing disk-bound applications and to find new applications for it. Nevertheless, developing correct programs that interact with non-volatile memory is by no means easy, since mainstream architectures provide rather weak persistency semantics and rather low-level and expensive mechanisms in order to avoid weak behaviors. This creates many opportunities for researchers in programming language semantics, logic, and verification to develop techniques to assist programmers writing NVM programs. This short paper and the associated talk outline the challenges caused by NVM and the research opportunities for PL researchers.
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Viktor Vafeiadis. The Challenges of Weak Persistency (Invited Talk). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 4:1-4:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{vafeiadis:LIPIcs.CALCO.2021.4,
  author =	{Vafeiadis, Viktor},
  title =	{{The Challenges of Weak Persistency}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{4:1--4:3},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.4},
  URN =		{urn:nbn:de:0030-drops-153593},
  doi =		{10.4230/LIPIcs.CALCO.2021.4},
  annote =	{Keywords: Weak Persistency, Non-Volatile Memory}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.5
Initial Algebras Without Iteration ((Co)algebraic pearls)

Authors: Jiří Adámek, Stefan Milius, and Lawrence S. Moss

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

Abstract
The Initial Algebra Theorem by Trnková et al. states, under mild assumptions, that an endofunctor has an initial algebra provided it has a pre-fixed point. The proof crucially depends on transfinitely iterating the functor and in fact shows that, equivalently, the (transfinite) initial-algebra chain stops. We give a constructive proof of the Initial Algebra Theorem that avoids transfinite iteration of the functor. For a given pre-fixed point A of the functor, it uses Pataraia’s theorem to obtain the least fixed point of a monotone function on the partial order formed by all subobjects of A. Thanks to properties of recursive coalgebras, this least fixed point yields an initial algebra. We obtain new results on fixed points and initial algebras in categories enriched over directed-complete partial orders, again without iteration. Using transfinite iteration we equivalently obtain convergence of the initial-algebra chain as an equivalent condition, overall yielding a streamlined version of the original proof.
Cite as

Jiří Adámek, Stefan Milius, and Lawrence S. Moss. Initial Algebras Without Iteration ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 5:1-5:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{adamek_et_al:LIPIcs.CALCO.2021.5,
  author =	{Ad\'{a}mek, Ji\v{r}{\'\i} and Milius, Stefan and Moss, Lawrence S.},
  title =	{{Initial Algebras Without Iteration}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{5:1--5:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.5},
  URN =		{urn:nbn:de:0030-drops-153606},
  doi =		{10.4230/LIPIcs.CALCO.2021.5},
  annote =	{Keywords: Initial algebra, Pataraia’s theorem, recursive coalgebra, initial-algebra chain}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.6
Which Categories Are Varieties? ((Co)algebraic pearls)

Authors: Jiří Adámek and Jiří Rosický

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

Abstract
Categories equivalent to single-sorted varieties of finitary algebras were characterized in the famous dissertation of Lawvere. We present a new proof of a slightly sharpened version: those are precisely the categories with kernel pairs and reflexive coequalizers having an abstractly finite, effective strong generator. A completely analogous result is proved for varieties of many-sorted algebras provided that there are only finitely many sorts. In case of infinitely many sorts a slightly weaker result is presented: instead of being abstractly finite, the generator is required to consist of finitely presentable objects.
Cite as

Jiří Adámek and Jiří Rosický. Which Categories Are Varieties? ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 6:1-6:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{adamek_et_al:LIPIcs.CALCO.2021.6,
  author =	{Ad\'{a}mek, Ji\v{r}{\'\i} and Rosick\'{y}, Ji\v{r}{\'\i}},
  title =	{{Which Categories Are Varieties?}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{6:1--6:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.6},
  URN =		{urn:nbn:de:0030-drops-153610},
  doi =		{10.4230/LIPIcs.CALCO.2021.6},
  annote =	{Keywords: variety, many-sorted algebra, abstractly finite object, effective object, strong generator}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2021.7
Tensor of Quantitative Equational Theories

Authors: Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin

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

Abstract
We develop a theory for the commutative combination of quantitative effects, their tensor, given as a combination of quantitative equational theories that imposes mutual commutation of the operations from each theory. As such, it extends the sum of two theories, which is just their unrestrained combination. Tensors of theories arise in several contexts; in particular, in the semantics of programming languages, the monad transformer for global state is given by a tensor. We show that under certain assumptions on the quantitative theories the free monad that arises from the tensor of two theories is the categorical tensor of the free monads on the theories. As an application, we provide the first algebraic axiomatizations of labelled Markov processes and Markov decision processes. Apart from the intrinsic interest in the axiomatizations, it is pleasing they are obtained compositionally by means of the sum and tensor of simpler quantitative equational theories.
Cite as

Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin. Tensor of Quantitative Equational Theories. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 7:1-7:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bacci_et_al:LIPIcs.CALCO.2021.7,
  author =	{Bacci, Giorgio and Mardare, Radu and Panangaden, Prakash and Plotkin, Gordon},
  title =	{{Tensor of Quantitative Equational Theories}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{7:1--7:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.7},
  URN =		{urn:nbn:de:0030-drops-153628},
  doi =		{10.4230/LIPIcs.CALCO.2021.7},
  annote =	{Keywords: Quantitative equational theories, Tensor, Monads, Quantitative Effects}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2021.8
Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

Authors: Jos C. M. Baeten, Cesare Carissimo, and Bas Luttik

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

Abstract
The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings. In the Reactive Turing Machine, transitions have labels to give a notion of interactivity. In the resulting process graph, we use bisimilarity instead of language equivalence. Subsequently, we considered other classical theorems and notions from automata theory and formal languages theory. In this paper, we consider the classical theorem of the correspondence between pushdown automata and context-free grammars. By changing the process operator of sequential composition to a sequencing operator with intermediate acceptance, we get a better correspondence in our setting. We find that the missing ingredient to recover the full correspondence is the addition of a notion of state awareness.
Cite as

Jos C. M. Baeten, Cesare Carissimo, and Bas Luttik. Pushdown Automata and Context-Free Grammars in Bisimulation Semantics. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 8:1-8:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baeten_et_al:LIPIcs.CALCO.2021.8,
  author =	{Baeten, Jos C. M. and Carissimo, Cesare and Luttik, Bas},
  title =	{{Pushdown Automata and Context-Free Grammars in Bisimulation Semantics}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{8:1--8:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.8},
  URN =		{urn:nbn:de:0030-drops-153632},
  doi =		{10.4230/LIPIcs.CALCO.2021.8},
  annote =	{Keywords: pushdown automaton, context-free grammar, bisimilarity, intermediate acceptance, state awareness}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.9
From Farkas' Lemma to Linear Programming: an Exercise in Diagrammatic Algebra ((Co)algebraic pearls)

Authors: Filippo Bonchi, Alessandro Di Giorgio, and Fabio Zanasi

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

Abstract
Farkas' lemma is a celebrated result on the solutions of systems of linear inequalities, which finds application pervasively in mathematics and computer science. In this work we show how to formulate and prove Farkas' lemma in diagrammatic polyhedral algebra, a sound and complete graphical calculus for polyhedra. Furthermore, we show how linear programs can be modeled within the calculus and how some famous duality results can be proved.
Cite as

Filippo Bonchi, Alessandro Di Giorgio, and Fabio Zanasi. From Farkas' Lemma to Linear Programming: an Exercise in Diagrammatic Algebra ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 9:1-9:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2021.9,
  author =	{Bonchi, Filippo and Di Giorgio, Alessandro and Zanasi, Fabio},
  title =	{{From Farkas' Lemma to Linear Programming: an Exercise in Diagrammatic Algebra}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{9:1--9:19},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.9},
  URN =		{urn:nbn:de:0030-drops-153643},
  doi =		{10.4230/LIPIcs.CALCO.2021.9},
  annote =	{Keywords: String diagrams, Farkas Lemma, Duality, Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2021.10
On Doctrines and Cartesian Bicategories

Authors: Filippo Bonchi, Alessio Santamaria, Jens Seeber, and Paweł Sobociński

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

Abstract
We study the relationship between cartesian bicategories and a specialisation of Lawvere’s hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the former in algebraic terms based on a string diagrammatic calculus, the latter in universal terms using the fundamental notion of adjoint functor. We prove that these two approaches are related by an adjunction, which can be strengthened to an equivalence by imposing further constraints on doctrines.
Cite as

Filippo Bonchi, Alessio Santamaria, Jens Seeber, and Paweł Sobociński. On Doctrines and Cartesian Bicategories. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 10:1-10:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2021.10,
  author =	{Bonchi, Filippo and Santamaria, Alessio and Seeber, Jens and Soboci\'{n}ski, Pawe{\l}},
  title =	{{On Doctrines and Cartesian Bicategories}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{10:1--10:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.10},
  URN =		{urn:nbn:de:0030-drops-153656},
  doi =		{10.4230/LIPIcs.CALCO.2021.10},
  annote =	{Keywords: Cartesian bicategories, elementary existential doctrines, string diagram}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.11
Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls)

Authors: Filippo Bonchi, Ana Sokolova, and Valeria Vignudelli

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

Abstract
We prove that every finitely generated convex set of finitely supported probability distributions has a unique base. We apply this result to provide an alternative proof of a recent result: the algebraic theory of convex semilattices presents the monad of convex sets of probability distributions.
Cite as

Filippo Bonchi, Ana Sokolova, and Valeria Vignudelli. Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 11:1-11:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2021.11,
  author =	{Bonchi, Filippo and Sokolova, Ana and Vignudelli, Valeria},
  title =	{{Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{11:1--11:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.11},
  URN =		{urn:nbn:de:0030-drops-153666},
  doi =		{10.4230/LIPIcs.CALCO.2021.11},
  annote =	{Keywords: Convex sets of distributions monad, Convex semilattices, Unique base}
}
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