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Documents authored by Pavlovic, Dusko

Document
DOI: 10.4230/LIPIcs.CONCUR.2017.24
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)

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@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-dev.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}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.130
Towards Concept Analysis in Categories: Limit Inferior as Algebra, Limit Superior as Coalgebra

Authors: Toshiki Kataoka and Dusko Pavlovic

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
While computer programs and logical theories begin by declaring the concepts of interest, be it as data types or as predicates, network computation does not allow such global declarations, and requires concept mining and concept analysis to extract shared semantics for different network nodes. Powerful semantic analysis systems have been the drivers of nearly all paradigm shifts on the web. In categorical terms, most of them can be described as bicompletions of enriched matrices, generalizing the Dedekind-MacNeille-style completions from posets to suitably enriched categories. Yet it has been well known for more than 40 years that ordinary categories themselves in general do not permit such completions. Armed with this new semantical view of Dedekind-MacNeille completions, and of matrix bicompletions, we take another look at this ancient mystery. It turns out that simple categorical versions of the limit superior and limit inferior operations characterize a general notion of Dedekind-MacNeille completion, that seems to be appropriate for ordinary categories, and boils down to the more familiar enriched versions when the limits inferior and superior coincide. This explains away the apparent gap among the completions of ordinary categories, and broadens the path towards categorical concept mining and analysis, opened in previous work.
Cite as

Toshiki Kataoka and Dusko Pavlovic. Towards Concept Analysis in Categories: Limit Inferior as Algebra, Limit Superior as Coalgebra. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 130-155, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kataoka_et_al:LIPIcs.CALCO.2015.130,
  author =	{Kataoka, Toshiki and Pavlovic, Dusko},
  title =	{{Towards Concept Analysis in Categories: Limit Inferior as Algebra, Limit Superior as Coalgebra}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{130--155},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.130},
  URN =		{urn:nbn:de:0030-drops-55317},
  doi =		{10.4230/LIPIcs.CALCO.2015.130},
  annote =	{Keywords: concept analysis, semantic indexing, category, completion, algebra}
}
Document
DOI: 10.4230/DagSemProc.09311.2
Geometry of abstraction in quantum computation

Authors: Dusko Pavlovic

Published in: Dagstuhl Seminar Proceedings, Volume 9311, Classical and Quantum Information Assurance Foundations and Practice (2010)

Abstract
Modern cryptography is based on various assumptions about computational hardness and feasibility. But while computability is a very robust notion (cf Church's Thesis), feasibility seems quite sensitive to the available computational resources. A prime example are, of course, quantum channels, which provide feasible solutions of some otherwise hard problems; but ants' pheromones, used as a computational resource, also provide feasible solutions of other hard problems. So at least in principle, modern cryptography is concerned with the power and availability of computational resources. The standard models, used in cryptography and in quantum computation, leave a lot to be desired in this respect. They do, of course, support many interesting solutions of deep problems; but besides the fundamental computational structures, they also capture some low level features of particular implementations. In technical terms of program semantics, our standard models are not *fully abstract*. (Related objections can be traced back to von Neumann's "I don't believe in Hilbert spaces" letters from 1937.) I shall report on some explorations towards extending the modeling tools of program semantics to develop a geometric language for quantum protocols and algorithms. Besides hiding the irrelevant implementation details, its abstract descriptions can also be used to explore simple nonstandard models. If the time permits, I shall describe a method to implement teleportation, as well as the hidden subgroup algorithms, using just abelian groups and relations.
Cite as

Dusko Pavlovic. Geometry of abstraction in quantum computation. In Classical and Quantum Information Assurance Foundations and Practice. Dagstuhl Seminar Proceedings, Volume 9311, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{pavlovic:DagSemProc.09311.2,
  author =	{Pavlovic, Dusko},
  title =	{{Geometry of abstraction in quantum computation}},
  booktitle =	{Classical and Quantum Information Assurance Foundations and Practice},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9311},
  editor =	{Samual L. Braunstein and Hoi-Kwong Lo and Kenny Paterson and Peter Ryan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09311.2},
  URN =		{urn:nbn:de:0030-drops-23623},
  doi =		{10.4230/DagSemProc.09311.2},
  annote =	{Keywords: Quantum algorithms, categorical semantics, Frobenius algebra, classical structure}
}
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