52 Search Results for "Ghica, Dan R."


Volume

LIPIcs, Volume 119

27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

CSL 2018, September 4-7, 2018, Birmingham, GB

Editors: Dan R. Ghica and Achim Jung

Document
Rewriting Modulo Traced Comonoid Structure

Authors: Dan R. Ghica and George Kaye

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)


Abstract
In this paper we adapt previous work on rewriting string diagrams using hypergraphs to the case where the underlying category has a traced comonoid structure, in which wires can be forked and the outputs of a morphism can be connected to its input. Such a structure is particularly interesting because any traced Cartesian (dataflow) category has an underlying traced comonoid structure. We show that certain subclasses of hypergraphs are fully complete for traced comonoid categories: that is to say, every term in such a category has a unique corresponding hypergraph up to isomorphism, and from every hypergraph with the desired properties, a unique term in the category can be retrieved up to the axioms of traced comonoid categories. We also show how the framework of double pushout rewriting (DPO) can be adapted for traced comonoid categories by characterising the valid pushout complements for rewriting in our setting. We conclude by presenting a case study in the form of recent work on an equational theory for sequential circuits: circuits built from primitive logic gates with delay and feedback. The graph rewriting framework allows for the definition of an operational semantics for sequential circuits.

Cite as

Dan R. Ghica and George Kaye. Rewriting Modulo Traced Comonoid Structure. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 14:1-14:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{ghica_et_al:LIPIcs.FSCD.2023.14,
  author =	{Ghica, Dan R. and Kaye, George},
  title =	{{Rewriting Modulo Traced Comonoid Structure}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.14},
  URN =		{urn:nbn:de:0030-drops-179983},
  doi =		{10.4230/LIPIcs.FSCD.2023.14},
  annote =	{Keywords: symmetric traced monoidal categories, string diagrams, graph rewriting, comonoid structure, double pushout rewriting}
}
Document
Functorial String Diagrams for Reverse-Mode Automatic Differentiation

Authors: Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)


Abstract
We formulate a reverse-mode automatic differentiation (RAD) algorithm for (applied) simply typed lambda calculus in the style of Pearlmutter and Siskind [Barak A. Pearlmutter and Jeffrey Mark Siskind, 2008], using the graphical formalism of string diagrams. Thanks to string diagram rewriting, we are able to formally prove for the first time the soundness of such an algorithm. Our approach requires developing a calculus of string diagrams with hierarchical features in the spirit of functorial boxes, in order to model closed monoidal (and cartesian closed) structure. To give an efficient yet principled implementation of the RAD algorithm, we use foliations of our hierarchical string diagrams.

Cite as

Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi. Functorial String Diagrams for Reverse-Mode Automatic Differentiation. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 6:1-6:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{alvarezpicallo_et_al:LIPIcs.CSL.2023.6,
  author =	{Alvarez-Picallo, Mario and Ghica, Dan and Sprunger, David and Zanasi, Fabio},
  title =	{{Functorial String Diagrams for Reverse-Mode Automatic Differentiation}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.6},
  URN =		{urn:nbn:de:0030-drops-174674},
  doi =		{10.4230/LIPIcs.CSL.2023.6},
  annote =	{Keywords: string diagrams, automatic differentiation, hierarchical hypergraphs}
}
Document
String Diagrams for Non-Strict Monoidal Categories

Authors: Paul Wilson, Dan Ghica, and Fabio Zanasi

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)


Abstract
Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied. In this paper, we provide a presentation by generators and relations of string diagrams for non-strict monoidal categories, and show how this construction can handle applications in domains such as digital circuits and programming languages. We prove the correctness of our construction, which yields a novel proof of Mac Lane’s strictness theorem. This in turn leads to an elementary graphical proof of Mac Lane’s coherence theorem, and in particular allows for the inductive construction of the canonical isomorphisms in a monoidal category.

Cite as

Paul Wilson, Dan Ghica, and Fabio Zanasi. String Diagrams for Non-Strict Monoidal Categories. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 37:1-37:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{wilson_et_al:LIPIcs.CSL.2023.37,
  author =	{Wilson, Paul and Ghica, Dan and Zanasi, Fabio},
  title =	{{String Diagrams for Non-Strict Monoidal Categories}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{37:1--37:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.37},
  URN =		{urn:nbn:de:0030-drops-174981},
  doi =		{10.4230/LIPIcs.CSL.2023.37},
  annote =	{Keywords: String Diagrams, Strictness, Coherence}
}
Document
Rewriting for Monoidal Closed Categories

Authors: Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)


Abstract
This paper develops a formal string diagram language for monoidal closed categories. Previous work has shown that string diagrams for freely generated symmetric monoidal categories can be viewed as hypergraphs with interfaces, and the axioms of these categories can be realized by rewriting systems. This work proposes hierarchical hypergraphs as a suitable formalization of string diagrams for monoidal closed categories. We then show double pushout rewriting captures the axioms of these closed categories.

Cite as

Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi. Rewriting for Monoidal Closed Categories. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 29:1-29:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{alvarezpicallo_et_al:LIPIcs.FSCD.2022.29,
  author =	{Alvarez-Picallo, Mario and Ghica, Dan and Sprunger, David and Zanasi, Fabio},
  title =	{{Rewriting for Monoidal Closed Categories}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.29},
  URN =		{urn:nbn:de:0030-drops-163108},
  doi =		{10.4230/LIPIcs.FSCD.2022.29},
  annote =	{Keywords: string diagrams, rewriting, hierarchical hypergraph, monoidal closed category}
}
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
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
A Typing Discipline for Hardware Interfaces

Authors: Jan de Muijnck-Hughes and Wim Vanderbauwhede

Published in: LIPIcs, Volume 134, 33rd European Conference on Object-Oriented Programming (ECOOP 2019)


Abstract
Modern Systems-on-a-Chip (SoC) are constructed by composition of IP (Intellectual Property) Cores with the communication between these IP Cores being governed by well described interaction protocols. However, there is a disconnect between the machine readable specification of these protocols and the verification of their implementation in known hardware description languages. Although tools can be written to address such separation of concerns, the tooling is often hand written and used to check hardware designs a posteriori. We have developed a dependent type-system and proof-of-concept modelling language to reason about the physical structure of hardware interfaces using user provided descriptions. Our type-system provides correct-by-construction guarantees that the interfaces on an IP Core will be well-typed if they adhere to a specified standard.

Cite as

Jan de Muijnck-Hughes and Wim Vanderbauwhede. A Typing Discipline for Hardware Interfaces. In 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 134, pp. 6:1-6:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{demuijnckhughes_et_al:LIPIcs.ECOOP.2019.6,
  author =	{de Muijnck-Hughes, Jan and Vanderbauwhede, Wim},
  title =	{{A Typing Discipline for Hardware Interfaces}},
  booktitle =	{33rd European Conference on Object-Oriented Programming (ECOOP 2019)},
  pages =	{6:1--6:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-111-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{134},
  editor =	{Donaldson, Alastair F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2019.6},
  URN =		{urn:nbn:de:0030-drops-107983},
  doi =		{10.4230/LIPIcs.ECOOP.2019.6},
  annote =	{Keywords: System-on-a-Chip, AXI, Dependent Types, Substructural Typing}
}
Document
Complete Volume
LIPIcs, Volume 119, CSL'18, Complete Volume

Authors: Dan Ghica and Achim Jung

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


Abstract
LIPIcs, Volume 119, CSL'18, Complete Volume

Cite as

Dan Ghica and Achim Jung. LIPIcs, Volume 119, CSL'18, Complete Volume. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@Proceedings{ghica_et_al:LIPIcs.CSL.2018,
  title =	{{LIPIcs, Volume 119, CSL'18, Complete Volume}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  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},
  URN =		{urn:nbn:de:0030-drops-97444},
  doi =		{10.4230/LIPIcs.CSL.2018},
  annote =	{Keywords: Theory of computation, Software and its engineering, Formal language definitions, Formal software verification}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Dan R. Ghica and Achim Jung

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


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

Cite as

Dan R. Ghica and Achim Jung. Front Matter, Table of Contents, Preface, Conference Organization. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 0:i-0:xiv, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{ghica_et_al:LIPIcs.CSL.2018.0,
  author =	{Ghica, Dan R. and Jung, Achim},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{0:i--0:xiv},
  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.2018.0},
  URN =		{urn:nbn:de:0030-drops-96679},
  doi =		{10.4230/LIPIcs.CSL.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
The Ackermann Award 2018

Authors: Dexter Kozen and Thomas Schwentick

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


Abstract
The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic in Computer Science. It is presented during the annual conference of the EACSL (CSL'xx). This contribution reports on the 2018 edition of the award.

Cite as

Dexter Kozen and Thomas Schwentick. The Ackermann Award 2018. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 1:1-1:5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{kozen_et_al:LIPIcs.CSL.2018.1,
  author =	{Kozen, Dexter and Schwentick, Thomas},
  title =	{{The Ackermann Award 2018}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{1:1--1:5},
  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.2018.1},
  URN =		{urn:nbn:de:0030-drops-96686},
  doi =		{10.4230/LIPIcs.CSL.2018.1},
  annote =	{Keywords: Ackermann Award}
}
Document
Relating Structure and Power: Comonadic Semantics for Computational Resources

Authors: Samson Abramsky and Nihil Shah

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


Abstract
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraïssé games, pebble games, and bisimulation games play a central role. We show how each of these types of games can be described in terms of an indexed family of comonads on the category of relational structures and homomorphisms. The index k is a resource parameter which bounds the degree of access to the underlying structure. The coKleisli categories for these comonads can be used to give syntax-free characterizations of a wide range of important logical equivalences. Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree-depth for the Ehrenfeucht-Fraïssé comonad, tree-width for the pebbling comonad, and synchronization-tree depth for the modal unfolding comonad. These results pave the way for systematic connections between two major branches of the field of logic in computer science which hitherto have been almost disjoint: categorical semantics, and finite and algorithmic model theory.

Cite as

Samson Abramsky and Nihil Shah. Relating Structure and Power: Comonadic Semantics for Computational Resources. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 2:1-2:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{abramsky_et_al:LIPIcs.CSL.2018.2,
  author =	{Abramsky, Samson and Shah, Nihil},
  title =	{{Relating Structure and Power: Comonadic Semantics for Computational Resources}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{2:1--2:17},
  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.2018.2},
  URN =		{urn:nbn:de:0030-drops-96698},
  doi =		{10.4230/LIPIcs.CSL.2018.2},
  annote =	{Keywords: Finite model theory, combinatorial games, Ehrenfeucht-Fra\"{i}ss\'{e} games, pebble games, bisimulation, comonads, coKleisli category, coalgebras of a comonad}
}
Document
Climbing up the Elementary Complexity Classes with Theories of Automatic Structures

Authors: Faried Abu Zaid, Dietrich Kuske, and Peter Lindner

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


Abstract
Automatic structures are structures that admit a finite presentation via automata. Their most prominent feature is that their theories are decidable. In the literature, one finds automatic structures with non-elementary theory (e.g., the complete binary tree with equal-level predicate) and automatic structures whose theories are at most 3-fold exponential (e.g., Presburger arithmetic or infinite automatic graphs of bounded degree). This observation led Durand-Gasselin to the question whether there are automatic structures of arbitrary high elementary complexity. We give a positive answer to this question. Namely, we show that for every h >=0 the forest of (infinitely many copies of) all finite trees of height at most h+2 is automatic and it's theory is complete for STA(*, exp_h(n, poly(n)), poly(n)), an alternating complexity class between h-fold exponential time and space. This exact determination of the complexity of the theory of these forests might be of independent interest.

Cite as

Faried Abu Zaid, Dietrich Kuske, and Peter Lindner. Climbing up the Elementary Complexity Classes with Theories of Automatic Structures. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 3:1-3:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{abuzaid_et_al:LIPIcs.CSL.2018.3,
  author =	{Abu Zaid, Faried and Kuske, Dietrich and Lindner, Peter},
  title =	{{Climbing up the Elementary Complexity Classes with Theories of Automatic Structures}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{3:1--3:16},
  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.2018.3},
  URN =		{urn:nbn:de:0030-drops-96701},
  doi =		{10.4230/LIPIcs.CSL.2018.3},
  annote =	{Keywords: Automatic Structures, Complexity Theory, Model Theory}
}
Document
High-Level Signatures and Initial Semantics

Authors: Benedikt Ahrens, André Hirschowitz, Ambroise Lafont, and Marco Maggesi

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


Abstract
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we consider a general notion of "signature" for specifying syntactic constructions. Our signatures subsume classical algebraic signatures (i.e., signatures for languages with variable binding, such as the pure lambda calculus) and extend to much more general examples. In the spirit of Initial Semantics, we define the "syntax generated by a signature" to be the initial object - if it exists - in a suitable category of models. Our notions of signature and syntax are suited for compositionality and provide, beyond the desired algebra of terms, a well-behaved substitution and the associated inductive/recursive principles. Our signatures are "general" in the sense that the existence of an associated syntax is not automatically guaranteed. In this work, we identify a large and simple class of signatures which do generate a syntax. This paper builds upon ideas from a previous attempt by Hirschowitz-Maggesi, which, in turn, was directly inspired by some earlier work of Ghani-Uustalu-Hamana and Matthes-Uustalu. The main results presented in the paper are computer-checked within the UniMath system.

Cite as

Benedikt Ahrens, André Hirschowitz, Ambroise Lafont, and Marco Maggesi. High-Level Signatures and Initial Semantics. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 4:1-4:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{ahrens_et_al:LIPIcs.CSL.2018.4,
  author =	{Ahrens, Benedikt and Hirschowitz, Andr\'{e} and Lafont, Ambroise and Maggesi, Marco},
  title =	{{High-Level Signatures and Initial Semantics}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{4:1--4:22},
  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.2018.4},
  URN =		{urn:nbn:de:0030-drops-96713},
  doi =		{10.4230/LIPIcs.CSL.2018.4},
  annote =	{Keywords: initial semantics, signatures, syntax, monadic substitution, computer-checked proofs}
}
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