39 Search Results for "Sobocinski, Pawel"


Volume

LIPIcs, Volume 35

6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

CALCO 2015, June 24-26, 2015, Nijmegen, The Netherlands

Editors: Lawrence S. Moss and Pawel Sobocinski

Document
The Produoidal Algebra of Process Decomposition

Authors: Matt Earnshaw, James Hefford, and Mario Román

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)


Abstract
We characterize a universal normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a decomposition, possibly containing missing parts. In particular, symmetric monoidal contexts coincide with monoidal lenses and endow them with a novel universal property. We apply this algebraic structure to the analysis of multi-party protocols in arbitrary theories of processes.

Cite as

Matt Earnshaw, James Hefford, and Mario Román. The Produoidal Algebra of Process Decomposition. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{earnshaw_et_al:LIPIcs.CSL.2024.25,
  author =	{Earnshaw, Matt and Hefford, James and Rom\'{a}n, Mario},
  title =	{{The Produoidal Algebra of Process Decomposition}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello 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.CSL.2024.25},
  URN =		{urn:nbn:de:0030-drops-196688},
  doi =		{10.4230/LIPIcs.CSL.2024.25},
  annote =	{Keywords: monoidal categories, profunctors, lenses, duoidal categories}
}
Document
String Diagrammatic Trace Theory

Authors: Matthew Earnshaw and Paweł Sobociński

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
We extend the theory of formal languages in monoidal categories to the multi-sorted, symmetric case, and show how this theory permits a graphical treatment of topics in concurrency. In particular, we show that Mazurkiewicz trace languages are precisely symmetric monoidal languages over monoidal distributed alphabets. We introduce symmetric monoidal automata, which define the class of regular symmetric monoidal languages. Furthermore, we prove that Zielonka’s asynchronous automata coincide with symmetric monoidal automata over monoidal distributed alphabets. Finally, we apply the string diagrams for symmetric premonoidal categories to derive serializations of traces.

Cite as

Matthew Earnshaw and Paweł Sobociński. String Diagrammatic Trace Theory. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 43:1-43:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{earnshaw_et_al:LIPIcs.MFCS.2023.43,
  author =	{Earnshaw, Matthew and Soboci\'{n}ski, Pawe{\l}},
  title =	{{String Diagrammatic Trace Theory}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.43},
  URN =		{urn:nbn:de:0030-drops-185770},
  doi =		{10.4230/LIPIcs.MFCS.2023.43},
  annote =	{Keywords: symmetric monoidal categories, Mazurkiewicz traces, asynchronous automata}
}
Document
Regular Monoidal Languages

Authors: Matthew Earnshaw and Paweł Sobociński

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of languages over string diagrams. We use the algebra of monoidal categories to investigate the properties of regular monoidal languages, and provide sufficient conditions for their recognizability by deterministic monoidal automata.

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Matthew Earnshaw and Paweł Sobociński. Regular Monoidal Languages. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 44:1-44:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{earnshaw_et_al:LIPIcs.MFCS.2022.44,
  author =	{Earnshaw, Matthew and Soboci\'{n}ski, Pawe{\l}},
  title =	{{Regular Monoidal Languages}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert 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.MFCS.2022.44},
  URN =		{urn:nbn:de:0030-drops-168425},
  doi =		{10.4230/LIPIcs.MFCS.2022.44},
  annote =	{Keywords: monoidal categories, string diagrams, formal language theory, cartesian restriction categories}
}
Document
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)


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@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
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
Compositional Modelling of Network Games

Authors: Elena Di Lavore, Jules Hedges, and Paweł Sobociński

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)


Abstract
The analysis of games played on graph-like structures is of increasing importance due to the prevalence of social networks, both virtual and physical, in our daily life. As well as being relevant in computer science, mathematical analysis and computer simulations of such distributed games are vital methodologies in economics, politics and epidemiology, amongst other fields. Our contribution is to give compositional semantics of a family of such games as a well-behaved mapping, a strict monoidal functor, from a category of open graphs (syntax) to a category of open games (semantics). As well as introducing the theoretical framework, we identify some applications of compositionality.

Cite as

Elena Di Lavore, Jules Hedges, and Paweł Sobociński. Compositional Modelling of Network Games. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 30:1-30:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{dilavore_et_al:LIPIcs.CSL.2021.30,
  author =	{Di Lavore, Elena and Hedges, Jules and Soboci\'{n}ski, Pawe{\l}},
  title =	{{Compositional Modelling of Network Games}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{30:1--30:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.30},
  URN =		{urn:nbn:de:0030-drops-134645},
  doi =		{10.4230/LIPIcs.CSL.2021.30},
  annote =	{Keywords: game theory, category theory, network games, open games, open graphs, compositionality}
}
Document
The Axiom of Choice in Cartesian Bicategories

Authors: Filippo Bonchi, Jens Seeber, and Paweł Sobociński

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
We argue that cartesian bicategories, often used as a general categorical algebra of relations, are also a natural setting for the study of the axiom of choice (AC). In this setting, AC manifests itself as an inequation asserting that every total relation contains a map. The generality of cartesian bicategories allows us to separate this formulation from other set-theoretically equivalent properties, for instance that epimorphisms split. Moreover, via a classification result, we show that cartesian bicategories satisfying choice tend to be those that arise from bicategories of spans.

Cite as

Filippo Bonchi, Jens Seeber, and Paweł Sobociński. The Axiom of Choice in Cartesian Bicategories. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2019.15,
  author =	{Bonchi, Filippo and Seeber, Jens and Soboci\'{n}ski, Pawe{\l}},
  title =	{{The Axiom of Choice in Cartesian Bicategories}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{15:1--15:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.15},
  URN =		{urn:nbn:de:0030-drops-114439},
  doi =		{10.4230/LIPIcs.CALCO.2019.15},
  annote =	{Keywords: Cartesian bicategories, Axiom of choice, string diagrams}
}
Document
Nominal String Diagrams

Authors: Samuel Balco and Alexander Kurz

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we develop the beginnings of a theory of monoidal categories internal in a symmetric monoidal category. As an instance, we obtain a notion of a nominal PROP as a PROP internal in nominal sets. A 2-dimensional calculus of simultaneous substitutions is an application.

Cite as

Samuel Balco and Alexander Kurz. Nominal String Diagrams. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{balco_et_al:LIPIcs.CALCO.2019.18,
  author =	{Balco, Samuel and Kurz, Alexander},
  title =	{{Nominal String Diagrams}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.18},
  URN =		{urn:nbn:de:0030-drops-114466},
  doi =		{10.4230/LIPIcs.CALCO.2019.18},
  annote =	{Keywords: string diagrams, nominal sets, separated product, simultaneous substitutions, internal category, monoidal category, internal monoidal categories, PROP}
}
Document
Tool Paper
CARTOGRAPHER: A Tool for String Diagrammatic Reasoning (Tool Paper)

Authors: Paweł Sobociński, Paul W. Wilson, and Fabio Zanasi

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
We introduce cartographer, a tool for editing and rewriting string diagrams of symmetric monoidal categories. Our approach is principled: the layout exploits the isomorphism between string diagrams and certain cospans of hypergraphs; the implementation of rewriting is based on the soundness and completeness of convex double-pushout rewriting for string diagram rewriting.

Cite as

Paweł Sobociński, Paul W. Wilson, and Fabio Zanasi. CARTOGRAPHER: A Tool for String Diagrammatic Reasoning (Tool Paper). In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 20:1-20:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{sobocinski_et_al:LIPIcs.CALCO.2019.20,
  author =	{Soboci\'{n}ski, Pawe{\l} and Wilson, Paul W. and Zanasi, Fabio},
  title =	{{CARTOGRAPHER: A Tool for String Diagrammatic Reasoning}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{20:1--20:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.20},
  URN =		{urn:nbn:de:0030-drops-114482},
  doi =		{10.4230/LIPIcs.CALCO.2019.20},
  annote =	{Keywords: tool, string diagram, symmetric monoidal category, graphical reasoning}
}
Document
SZX-Calculus: Scalable Graphical Quantum Reasoning

Authors: Titouan Carette, Dominic Horsman, and Simon Perdrix

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that captures graphically the fundamental properties of quantum mechanics through its complete set of rewrite rules. The ZX-calculus is, however, a low level language, with each wire representing a single qubit. This limits its ability to handle large and elaborate quantum evolutions. We extend the ZX-calculus to registers of qubits and allow compact representation of sub-diagrams via binary matrices. We show soundness and completeness of the SZX-calculus and provide two examples of applications, for graph states and error correcting codes.

Cite as

Titouan Carette, Dominic Horsman, and Simon Perdrix. SZX-Calculus: Scalable Graphical Quantum Reasoning. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{carette_et_al:LIPIcs.MFCS.2019.55,
  author =	{Carette, Titouan and Horsman, Dominic and Perdrix, Simon},
  title =	{{SZX-Calculus: Scalable Graphical Quantum Reasoning}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.55},
  URN =		{urn:nbn:de:0030-drops-109999},
  doi =		{10.4230/LIPIcs.MFCS.2019.55},
  annote =	{Keywords: Quantum computing, categorical quantum mechanics, completeness, scalability}
}
Document
Bialgebraic Semantics for String Diagrams

Authors: Filippo Bonchi, Robin Piedeleu, Pawel Sobocinski, and Fabio Zanasi

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)


Abstract
Turi and Plotkin’s bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as a monad) and its dynamics (an endofunctor). This setup is instrumental in showing that a semantic specification (a coalgebra) satisfies desirable properties: in particular, that it is compositional. In this work, we use the bialgebraic approach to derive well-behaved structural operational semantics of string diagrams, a graphical syntax that is increasingly used in the study of interacting systems across different disciplines. Our analysis relies on representing the two-dimensional operations underlying string diagrams in various categories as a monad, and their bialgebraic semantics in terms of a distributive law for that monad. As a proof of concept, we provide bialgebraic compositional semantics for a versatile string diagrammatic language which has been used to model both signal flow graphs (control theory) and Petri nets (concurrency theory). Moreover, our approach reveals a correspondence between two different interpretations of the Frobenius equations on string diagrams and two synchronisation mechanisms for processes, à la Hoare and à la Milner.

Cite as

Filippo Bonchi, Robin Piedeleu, Pawel Sobocinski, and Fabio Zanasi. Bialgebraic Semantics for String Diagrams. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bonchi_et_al:LIPIcs.CONCUR.2019.37,
  author =	{Bonchi, Filippo and Piedeleu, Robin and Sobocinski, Pawel and Zanasi, Fabio},
  title =	{{Bialgebraic Semantics for String Diagrams}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{37:1--37:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.37},
  URN =		{urn:nbn:de:0030-drops-109398},
  doi =		{10.4230/LIPIcs.CONCUR.2019.37},
  annote =	{Keywords: String Diagram, Structural Operational Semantics, Bialgebraic semantics}
}
Document
Rule Algebras for Adhesive Categories

Authors: Nicolas Behr and Pawel Sobocinski

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)


Abstract
We show that every adhesive category gives rise to an associative algebra of rewriting rules induced by the notion of double-pushout (DPO) rewriting and the associated notion of concurrent production. In contrast to the original formulation of rule algebras in terms of relations between (a concrete notion of) graphs, here we work in an abstract categorical setting. Doing this, we extend the classical concurrency theorem of DPO rewriting and show that the composition of DPO rules along abstract dependency relations is, in a natural sense, an associative operation. If in addition the adhesive category possesses a strict initial object, the resulting rule algebra is also unital. We demonstrate that in this setting the canonical representation of the rule algebras is obtainable, which opens the possibility of applying the concept to define and compute the evolution of statistical moments of observables in stochastic DPO rewriting systems.

Cite as

Nicolas Behr and Pawel Sobocinski. Rule Algebras for Adhesive Categories. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 11:1-11:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{behr_et_al:LIPIcs.CSL.2018.11,
  author =	{Behr, Nicolas and Sobocinski, Pawel},
  title =	{{Rule Algebras for Adhesive Categories}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.11},
  URN =		{urn:nbn:de:0030-drops-96781},
  doi =		{10.4230/LIPIcs.CSL.2018.11},
  annote =	{Keywords: Adhesive categories, rule algebras, Double Pushout (DPO) rewriting}
}
Document
Graphical Conjunctive Queries

Authors: Filippo Bonchi, Jens Seeber, and Pawel Sobocinski

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)


Abstract
The Calculus of Conjunctive Queries (CCQ) has foundational status in database theory. A celebrated theorem of Chandra and Merlin states that CCQ query inclusion is decidable. Its proof transforms logical formulas to graphs: each query has a natural model - a kind of graph - and query inclusion reduces to the existence of a graph homomorphism between natural models. We introduce the diagrammatic language Graphical Conjunctive Queries (GCQ) and show that it has the same expressivity as CCQ. GCQ terms are string diagrams, and their algebraic structure allows us to derive a sound and complete axiomatisation of query inclusion, which turns out to be exactly Carboni and Walters' notion of cartesian bicategory of relations. Our completeness proof exploits the combinatorial nature of string diagrams as (certain cospans of) hypergraphs: Chandra and Merlin's insights inspire a theorem that relates such cospans with spans. Completeness and decidability of the (in)equational theory of GCQ follow as a corollary. Categorically speaking, our contribution is a model-theoretic completeness theorem of free cartesian bicategories (on a relational signature) for the category of sets and relations.

Cite as

Filippo Bonchi, Jens Seeber, and Pawel Sobocinski. Graphical Conjunctive Queries. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 13:1-13:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{bonchi_et_al:LIPIcs.CSL.2018.13,
  author =	{Bonchi, Filippo and Seeber, Jens and Sobocinski, Pawel},
  title =	{{Graphical Conjunctive Queries}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.13},
  URN =		{urn:nbn:de:0030-drops-96805},
  doi =		{10.4230/LIPIcs.CSL.2018.13},
  annote =	{Keywords: conjunctive query inclusion, string diagrams, cartesian bicategories}
}
Document
Refinement for Signal Flow Graphs

Authors: Filippo Bonchi, Joshua Holland, Dusko Pavlovic, and Pawel Sobocinski

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)


Abstract
The symmetric monoidal theory of Interacting Hopf Algebras provides a sound and complete axiomatisation for linear relations over a given field. As is the case for ordinary relations, linear relations have a natural order that coincides with inclusion. In this paper, we give a presentation for this ordering by extending the theory of Interacting Hopf Algebras with a single additional inequation. We show that the extended theory gives rise to an abelian bicategory—a concept due to Carboni and Walters—and highlight similarities with the algebra of relations. Most importantly, the ordering leads to a well-behaved notion of refinement for signal flow graphs.

Cite as

Filippo Bonchi, Joshua Holland, Dusko Pavlovic, and Pawel Sobocinski. Refinement for Signal Flow Graphs. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 24:1-24:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{bonchi_et_al:LIPIcs.CONCUR.2017.24,
  author =	{Bonchi, Filippo and Holland, Joshua and Pavlovic, Dusko and Sobocinski, Pawel},
  title =	{{Refinement for Signal Flow Graphs}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.24},
  URN =		{urn:nbn:de:0030-drops-77758},
  doi =		{10.4230/LIPIcs.CONCUR.2017.24},
  annote =	{Keywords: Signal flow graphs, refinement, operational semantics, string diagrams, symmetric monoidal inequality theory}
}
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