2 Search Results for "Williams, Christian"

Document
DOI: 10.4230/LIPIcs.CALCO.2021.20
The Open Algebraic Path Problem

Authors: Jade Master

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

Abstract
The algebraic path problem provides a general setting for shortest path algorithms in optimization and computer science. We explain the universal property of solutions to the algebraic path problem by constructing a left adjoint functor whose values are given by these solutions. This paper extends the algebraic path problem to networks equipped with input and output boundaries. We show that the algebraic path problem is functorial as a mapping from a double category whose horizontal composition is gluing of open networks. We introduce functional open matrices, for which the functoriality of the algebraic path problem has a more practical expression.
Cite as

Jade Master. The Open Algebraic Path Problem. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{master:LIPIcs.CALCO.2021.20,
  author =	{Master, Jade},
  title =	{{The Open Algebraic Path Problem}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.20},
  URN =		{urn:nbn:de:0030-drops-153754},
  doi =		{10.4230/LIPIcs.CALCO.2021.20},
  annote =	{Keywords: The Algebraic Path Problem, Open Systems, Shortest Paths, Categorical Semantics, Compositionality}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.88
Abstract Congruence Criteria for Weak Bisimilarity

Authors: Stelios Tsampas, Christian Williams, Andreas Nuyts, Dominique Devriese, and Frank Piessens

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

Abstract
We introduce three general compositionality criteria over operational semantics and prove that, when all three are satisfied together, they guarantee weak bisimulation being a congruence. Our work is founded upon Turi and Plotkin’s mathematical operational semantics and the coalgebraic approach to weak bisimulation by Brengos. We demonstrate each criterion with various examples of success and failure and establish a formal connection with the simply WB cool rule format of Bloom and van Glabbeek. In addition, we show that the three criteria induce lax models in the sense of Bonchi et al.
Cite as

Stelios Tsampas, Christian Williams, Andreas Nuyts, Dominique Devriese, and Frank Piessens. Abstract Congruence Criteria for Weak Bisimilarity. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 88:1-88:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{tsampas_et_al:LIPIcs.MFCS.2021.88,
  author =	{Tsampas, Stelios and Williams, Christian and Nuyts, Andreas and Devriese, Dominique and Piessens, Frank},
  title =	{{Abstract Congruence Criteria for Weak Bisimilarity}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{88:1--88:23},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.88},
  URN =		{urn:nbn:de:0030-drops-145281},
  doi =		{10.4230/LIPIcs.MFCS.2021.88},
  annote =	{Keywords: Structural Operational Semantics, distributive laws, weak bisimilarity}
}
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