2 Search Results for "Borlido, Célia"

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

DOI: 10.4230/LIPIcs.ICALP.2020.135

Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic

Authors: Lê Thành Dũng Nguyễn and Pierre Pradic

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract

We give a characterization of star-free languages in a λ-calculus with support for non-commutative affine types (in the sense of linear logic), via the algebraic characterization of the former using aperiodic monoids. When the type system is made commutative, we show that we get regular languages instead. A key ingredient in our approach – that it shares with higher-order model checking – is the use of Church encodings for inputs and outputs. Our result is, to our knowledge, the first use of non-commutativity in implicit computational complexity.

Cite as

Lê Thành Dũng Nguyễn and Pierre Pradic. Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 135:1-135:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{nguyen_et_al:LIPIcs.ICALP.2020.135,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, Pierre},
  title =	{{Implicit Automata in Typed \lambda-Calculi I: Aperiodicity in a Non-Commutative Logic}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{135:1--135:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.135},
  URN =		{urn:nbn:de:0030-drops-125426},
  doi =		{10.4230/LIPIcs.ICALP.2020.135},
  annote =	{Keywords: Church encodings, ordered linear types, star-free languages}
}

Document

DOI: 10.4230/LIPIcs.CSL.2017.13

Stone Duality and the Substitution Principle

Authors: Célia Borlido, Silke Czarnetzki, Mai Gehrke, and Andreas Krebs

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

In this paper we relate two generalisations of the finite monoid recognisers of automata theory for the study of circuit complexity classes: Boolean spaces with internal monoids and typed monoids. Using the setting of stamps, this allows us to generalise a number of results from algebraic automata theory as it relates to Büchi's logic on words. We obtain an Eilenberg theorem, a substitution principle based on Stone duality, a block product principle for typed stamps and, as our main result, a topological semidirect product construction, which corresponds to the application of a general form of quantification. These results provide tools for the study of language classes given by logic fragments such as the Boolean circuit complexity classes.

Cite as

Célia Borlido, Silke Czarnetzki, Mai Gehrke, and Andreas Krebs. Stone Duality and the Substitution Principle. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{borlido_et_al:LIPIcs.CSL.2017.13,
  author =	{Borlido, C\'{e}lia and Czarnetzki, Silke and Gehrke, Mai and Krebs, Andreas},
  title =	{{Stone Duality and the Substitution Principle}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.13},
  URN =		{urn:nbn:de:0030-drops-77060},
  doi =		{10.4230/LIPIcs.CSL.2017.13},
  annote =	{Keywords: C-variety of languages, typed monoid, Boolean space with an internal monoid, substitution principle, semidirect product}
}

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