DROPS

Volume

LIPIcs, Volume 202

46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

MFCS 2021, August 23-27, 2021, Tallinn, Estonia

Editors: Filippo Bonchi and Simon J. Puglisi

Volume

LIPIcs, Volume 72

7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)

CALCO 2017, June 12-16, 2017, Ljubljana, Slovenia

Editors: Filippo Bonchi and Barbara König

Document

DOI: 10.4230/LIPIcs.FSCD.2024.5

The Flower Calculus

Authors: Pablo Donato

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

Abstract

We introduce the flower calculus, a deep inference proof system for intuitionistic first-order logic inspired by Peirce’s existential graphs. It works as a rewriting system over inductive objects called "flowers", that enjoy both a graphical interpretation as topological diagrams, and a textual presentation as nested sequents akin to coherent formulas. Importantly, the calculus dispenses completely with the traditional notion of symbolic connective, operating solely on nested flowers containing atomic predicates. We prove both the soundness of the full calculus and the completeness of an analytic fragment with respect to Kripke semantics. This provides to our knowledge the first analyticity result for a proof system based on existential graphs, adapting semantic cut-elimination techniques to a deep inference setting. Furthermore, the kernel of rules targetted by completeness is fully invertible, a desirable property for both automated and interactive proof search.

Cite as

Pablo Donato. The Flower Calculus. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{donato:LIPIcs.FSCD.2024.5,
  author =	{Donato, Pablo},
  title =	{{The Flower Calculus}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{5:1--5:24},
  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.2024.5},
  URN =		{urn:nbn:de:0030-drops-203343},
  doi =		{10.4230/LIPIcs.FSCD.2024.5},
  annote =	{Keywords: deep inference, graphical calculi, existential graphs, intuitionistic logic, Kripke semantics, cut-elimination}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.17

A Categorical Approach to DIBI Models

Authors: Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi

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

Abstract

The logic of Dependence and Independence Bunched Implications (DIBI) is a logic to reason about conditional independence (CI); for instance, DIBI formulas can characterise CI in discrete probability distributions and in relational databases, using a probabilistic DIBI model and a similarly-constructed relational model. Despite the similarity of the two models, there lacks a uniform account. As a result, the laborious case-by-case verification of the frame conditions required for constructing new models hinders them from generalising the results to CI in other useful models such that continuous distribution. In this paper, we develop an abstract framework for systematically constructing DIBI models, using category theory as the unifying mathematical language. We show that DIBI models arise from arbitrary symmetric monoidal categories with copy-discard structure. In particular, we use string diagrams - a graphical presentation of monoidal categories - to give a uniform definition of the parallel composition and subkernel relation in DIBI models. Our approach not only generalises known models, but also yields new models of interest and reduces properties of DIBI models to structures in the underlying categories. Furthermore, our categorical framework enables a comparison between string diagrammatic approaches to CI in the literature and a logical notion of CI, defined in terms of the satisfaction of specific DIBI formulas. We show that the logical notion is an extension of string diagrammatic CI under reasonable conditions.

Cite as

Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi. A Categorical Approach to DIBI Models. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{gu_et_al:LIPIcs.FSCD.2024.17,
  author =	{Gu, Tao and Bao, Jialu and Hsu, Justin and Silva, Alexandra and Zanasi, Fabio},
  title =	{{A Categorical Approach to DIBI Models}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{17:1--17:20},
  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.2024.17},
  URN =		{urn:nbn:de:0030-drops-203469},
  doi =		{10.4230/LIPIcs.FSCD.2024.17},
  annote =	{Keywords: Conditional Independence, Dependence Independence Bunched Implications, String Diagrams, Markov Categories}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.130

Function Spaces for Orbit-Finite Sets

Authors: Mikołaj Bojańczyk, Lê Thành Dũng (Tito) Nguyễn, and Rafał Stefański

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are orbit-finite sets, then the space of finitely supported functions from X to Y is not orbit-finite. We propose a solution to this problem inspired by linear logic.

Cite as

Mikołaj Bojańczyk, Lê Thành Dũng (Tito) Nguyễn, and Rafał Stefański. Function Spaces for Orbit-Finite Sets. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 130:1-130:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bojanczyk_et_al:LIPIcs.ICALP.2024.130,
  author =	{Boja\'{n}czyk, Miko{\l}aj and Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito) and Stefa\'{n}ski, Rafa{\l}},
  title =	{{Function Spaces for Orbit-Finite Sets}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{130:1--130:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.130},
  URN =		{urn:nbn:de:0030-drops-202730},
  doi =		{10.4230/LIPIcs.ICALP.2024.130},
  annote =	{Keywords: Orbit-finite sets, automata, linear types, game semantics}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.149

A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions

Authors: Wojciech Różowski

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

Deterministic automata have been traditionally studied through the point of view of language equivalence, but another perspective is given by the canonical notion of shortest-distinguishing-word distance quantifying the of states. Intuitively, the longer the word needed to observe a difference between two states, then the closer their behaviour is. In this paper, we give a sound and complete axiomatisation of shortest-distinguishing-word distance between regular languages. Our axiomatisation relies on a recently developed quantitative analogue of equational logic, allowing to manipulate rational-indexed judgements of the form e ≡_ε f meaning term e is approximately equivalent to term f within the error margin of ε. The technical core of the paper is dedicated to the completeness argument that draws techniques from order theory and Banach spaces to simplify the calculation of the behavioural distance to the point it can be then mimicked by axiomatic reasoning.

Cite as

Wojciech Różowski. A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 149:1-149:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rozowski:LIPIcs.ICALP.2024.149,
  author =	{R\'{o}\.{z}owski, Wojciech},
  title =	{{A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{149:1--149:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.149},
  URN =		{urn:nbn:de:0030-drops-202920},
  doi =		{10.4230/LIPIcs.ICALP.2024.149},
  annote =	{Keywords: Regular Expressions, Behavioural Distances, Quantitative Equational Theories}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.152

On Homomorphism Indistinguishability and Hypertree Depth

Authors: Benjamin Scheidt

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

GC^k is a logic introduced by Scheidt and Schweikardt (2023) to express properties of hypergraphs. It is similar to first-order logic with counting quantifiers (C) adapted to the hypergraph setting. It has distinct sets of variables for vertices and for hyperedges and requires vertex variables to be guarded by hyperedge variables on every quantification. We prove that two hypergraphs G, H satisfy the same sentences in the logic GC^k with guard depth at most k if, and only if, they are homomorphism indistinguishable over the class of hypergraphs of strict hypertree depth at most k. This lifts the analogous result for tree depth ≤ k and sentences of first-order logic with counting quantifiers of quantifier rank at most k due to Grohe (2020) from graphs to hypergraphs. The guard depth of a formula is the quantifier rank with respect to hyperedge variables, and strict hypertree depth is a restriction of hypertree depth as defined by Adler, Gavenčiak and Klimošová (2012). To justify this restriction, we show that for every H, the strict hypertree depth of H is at most 1 larger than its hypertree depth, and we give additional evidence that strict hypertree depth can be viewed as a reasonable generalisation of tree depth for hypergraphs.

Cite as

Benjamin Scheidt. On Homomorphism Indistinguishability and Hypertree Depth. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 152:1-152:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{scheidt:LIPIcs.ICALP.2024.152,
  author =	{Scheidt, Benjamin},
  title =	{{On Homomorphism Indistinguishability and Hypertree Depth}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{152:1--152:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.152},
  URN =		{urn:nbn:de:0030-drops-202958},
  doi =		{10.4230/LIPIcs.ICALP.2024.152},
  annote =	{Keywords: homomorphism indistinguishability, counting logics, guarded logics, hypergraphs, incidence graphs, tree depth, elimination forest, hypertree width}
}

Document

DOI: 10.4230/LIPIcs.FSTTCS.2021.40

Diagrammatic Polyhedral Algebra

Authors: Filippo Bonchi, Alessandro Di Giorgio, and Paweł Sobociński

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract

We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the prop of polyhedra.

Cite as

Filippo Bonchi, Alessandro Di Giorgio, and Paweł Sobociński. Diagrammatic Polyhedral Algebra. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{bonchi_et_al:LIPIcs.FSTTCS.2021.40,
  author =	{Bonchi, Filippo and Di Giorgio, Alessandro and Soboci\'{n}ski, Pawe{\l}},
  title =	{{Diagrammatic Polyhedral Algebra}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{40:1--40:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.40},
  URN =		{urn:nbn:de:0030-drops-155511},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.40},
  annote =	{Keywords: String diagrams, Polyhedral cones, Polyhedra}
}

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)

Copy BibTex To Clipboard

@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)

Copy BibTex To Clipboard

@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)

Copy BibTex To Clipboard

@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}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.MFCS.2021

LIPIcs, Volume 202, MFCS 2021, Complete Volume

Authors: Filippo Bonchi and Simon J. Puglisi

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

LIPIcs, Volume 202, MFCS 2021, Complete Volume

Cite as

46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 1-1560, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@Proceedings{bonchi_et_al:LIPIcs.MFCS.2021,
  title =	{{LIPIcs, Volume 202, MFCS 2021, Complete Volume}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{1--1560},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021},
  URN =		{urn:nbn:de:0030-drops-144396},
  doi =		{10.4230/LIPIcs.MFCS.2021},
  annote =	{Keywords: LIPIcs, Volume 202, MFCS 2021, Complete Volume}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.MFCS.2021.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Filippo Bonchi and Simon J. Puglisi

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{bonchi_et_al:LIPIcs.MFCS.2021.0,
  author =	{Bonchi, Filippo and Puglisi, Simon J.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.0},
  URN =		{urn:nbn:de:0030-drops-144409},
  doi =		{10.4230/LIPIcs.MFCS.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2021.1

Non-Axiomatizability of the Equational Theories of Positive Relation Algebras (Invited Talk)

Authors: Amina Doumane

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

In the literature, there are two ways to show that the equational theory of relations over a given signature is not finitely axiomatizable. The first-one is based on games and a construction called Rainbow construction. This method is very technical but it shows a strong result: the equational theory cannot be axiomatized by any finite set of first-order formulas. There is another method, based on a graph characterization of the equational theory of relations, which is easier to get and to understand, but proves a weaker result: the equational theory cannot be axiomatized by any finite set of equations. In this presentation, I will show how to complete the second technique to get the stronger result of non-axiomatizability by first-order formulas.

Cite as

Amina Doumane. Non-Axiomatizability of the Equational Theories of Positive Relation Algebras (Invited Talk). In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{doumane:LIPIcs.MFCS.2021.1,
  author =	{Doumane, Amina},
  title =	{{Non-Axiomatizability of the Equational Theories of Positive Relation Algebras}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.1},
  URN =		{urn:nbn:de:0030-drops-144417},
  doi =		{10.4230/LIPIcs.MFCS.2021.1},
  annote =	{Keywords: Relation algebra, Graph homomorphism, Equational theories, First-order logic}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2021.2

A Deep Dive into the Weisfeiler-Leman Algorithm (Invited Talk)

Authors: Martin Grohe

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

The Weisfeiler-Leman algorithm is a well-known combinatorial graph isomorphism test going back to work of Weisfeiler and Leman in the late 1960s. The algorithm has a surprising number of seemingly unrelated characterisations in terms of logic, algebra, linear and semi-definite programming, and graph homomorphisms. Due to its simplicity and efficiency, it is an important subroutine of all modern graph isomorphism tools. In recent years, further applications in linear optimisation, probabilistic inference, and machine learning have surfaced. In my talk, I will introduce the Weisfeiler-Leman algorithm and some extensions. I will discuss its expressiveness and the various characterisations, and I will speak about its applications.

Cite as

Martin Grohe. A Deep Dive into the Weisfeiler-Leman Algorithm (Invited Talk). In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{grohe:LIPIcs.MFCS.2021.2,
  author =	{Grohe, Martin},
  title =	{{A Deep Dive into the Weisfeiler-Leman Algorithm}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.2},
  URN =		{urn:nbn:de:0030-drops-144429},
  doi =		{10.4230/LIPIcs.MFCS.2021.2},
  annote =	{Keywords: Weisfeiler-Leman algorithm, graph isomorphism, counting homomorphisms, finite variable logics}
}

140 Search Results for "Bonchi, Filippo"

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as