Volume

Dagstuhl Seminar Proceedings, Volume 6341

Publication Details

  • published at: 2007-02-26
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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Document
DOI: 10.4230/DagSemProc.06341.1
06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality

Authors: Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, and Dieter Spreen

Abstract
From 20.08.06 to 25.08.06, the Dagstuhl Seminar 06341 ``Computational Structures for Modelling Space, Time and Causality'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, and Dieter Spreen. 06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{kopperman_et_al:DagSemProc.06341.1,
  author =	{Kopperman, Ralph and Panangaden, Prakash and Smyth, Michael B. and Spreen, Dieter},
  title =	{{06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--23},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.1},
  URN =		{urn:nbn:de:0030-drops-9000},
  doi =		{10.4230/DagSemProc.06341.1},
  annote =	{Keywords: Borel hierarchy, causets, Chu spaces, computations in higher types, computable analysis, constructive topology, differential calculus, digital topology, dihomotopy, domain theory, domain representation, formal topology, higher dimensional automata, mereo\backslash-topology, partial metrics}
}
Document
DOI: 10.4230/DagSemProc.06341.2
A convenient category of domains

Authors: Ingo Battenfeld, Matthias Schröder, and Alex Simpson

Abstract
We motivate and define a category of "topological domains", whose objects are certain topological spaces, generalising the usual $omega$-continuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also supports the construction of free algebras for (in)equational theories, provides a model of parametric polymorphism, and can be used as the basis for a theory of computability. This answers a question of Gordon Plotkin, who asked whether it was possible to construct a category of domains combining such properties.
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Ingo Battenfeld, Matthias Schröder, and Alex Simpson. A convenient category of domains. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{battenfeld_et_al:DagSemProc.06341.2,
  author =	{Battenfeld, Ingo and Schr\"{o}der, Matthias and Simpson, Alex},
  title =	{{A convenient category of domains}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.2},
  URN =		{urn:nbn:de:0030-drops-8945},
  doi =		{10.4230/DagSemProc.06341.2},
  annote =	{Keywords: Domain theory, topology of datatypes}
}
Document
DOI: 10.4230/DagSemProc.06341.3
Closure and Causality

Authors: John L. Pfaltz

Abstract
We present a model of causality which is defined by the intersection of two distinct closure systems, ${cal I}$ and ${cal T}$. Next we present empirical evidence to demonstrate that this model has practical validity by examining computer trace data to reveal causal dependencies between individual code modules. From over 498,000 events in the transaction manager of an open source system we tease out 66 apparent causal dependencies. Finally, we explore how to mathematically model the transformation of a causal topology resulting from unforlding events.
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John L. Pfaltz. Closure and Causality. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{pfaltz:DagSemProc.06341.3,
  author =	{Pfaltz, John L.},
  title =	{{Closure and Causality}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.3},
  URN =		{urn:nbn:de:0030-drops-8978},
  doi =		{10.4230/DagSemProc.06341.3},
  annote =	{Keywords: Closure, causality, antimatroid, temporal, software engineering}
}
Document
DOI: 10.4230/DagSemProc.06341.4
Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces

Authors: Howard Blair

Abstract
We unify a variety of continuous and discrete types of change of state phenomena using a scheme whose instances are differential calculi on structures that embrace both topological spaces and graphs as well as hybrid ramifications of such structures. These calculi include the elementary differential calculus on real and complex vector spaces. One class of spaces that has been increasingly receiving attention in recent years is the class of convergence spaces [cf. Heckmann, R., TCS v.305, (159--186)(2003)]. The class of convergence spaces together with the continuous functions among convergence spaces forms a Cartesian-closed category CONV that contains as full subcategories both the category TOP of topological spaces and an embedding of the category DIGRAPH of reflexive directed graphs. (More can importantly be said about these embeddings.) These properties of CONV serve to assure that we can construct continuous products of continuous functions, and that there is always at least one convergence structure available in function spaces with respect to which the operations of function application and composition are continuous. The containment of TOP and DIGRAPH in CONV allows to combine arbitrary topological spaces with discrete structures (as represented by digraphs) to obtain hybrid structures, which generally are not topological spaces. We give a differential calculus scheme in CONV that addresses three issues in particular. 1. For convergence spaces $X$ and $Y$ and function $f: X longrightarrow Y$, the scheme gives necessary and sufficient conditions for a candidate differential $df: X longrightarrow Y$ to be a (not necessarily "the", depending on the spaces involved) differential of $f$ at $x_0$. 2. The chain rule holds and the differential relation between functions distributes over Cartesian products: e.g. if $Df$, $Dg$ and $Dh$ are, respectively, differentials of $f$ at $(g(x_0),h(x_0))$ and $g$ and $h$ at $x_0$, then $Df circ (Dg times Dh)$ is a differential of $f circ (g times h)$ at $x_0$. 3. When specialized to real and complex vector spaces, the scheme is in agreement with ordinary elementary differential calculus on these spaces. Moreover, with two additional constraints having to do with self-differentiation of differentials and translation invariance (for example, a linear operator on, say, $C^2$, is its own differential everywhere) there is a (unique) maximum differential calculus in CONV.
Cite as

Howard Blair. Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{blair:DagSemProc.06341.4,
  author =	{Blair, Howard},
  title =	{{Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.4},
  URN =		{urn:nbn:de:0030-drops-8956},
  doi =		{10.4230/DagSemProc.06341.4},
  annote =	{Keywords: Hybrid space, convergence space, differential, calculus, chain rule, hybrid dynamical system, discrete structure, topological space}
}
Document
DOI: 10.4230/DagSemProc.06341.5
Enriched categories and models for spaces of dipaths

Authors: Timothy Porter

Abstract
Partially ordered sets, causets, partially ordered spaces and their local counterparts are now often used to model systems in computer science and theoretical physics. The order models `time' which is often not globally given. In this setting directed paths are important objects of study as they correspond to an evolving state or particle traversing the system. Many physical problems rely on the analysis of models of the path space of space-time manifold. Many problems in concurrent systems use `spaces' of paths in a system. Here we review some ideas from algebraic topology that suggest how to model the dipath space of a pospace by a simplicially enriched category.
Cite as

Timothy Porter. Enriched categories and models for spaces of dipaths. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{porter:DagSemProc.06341.5,
  author =	{Porter, Timothy},
  title =	{{Enriched categories and models for spaces of dipaths}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.5},
  URN =		{urn:nbn:de:0030-drops-8989},
  doi =		{10.4230/DagSemProc.06341.5},
  annote =	{Keywords: Enriched category}
}
Document
DOI: 10.4230/DagSemProc.06341.6
Instant topological relationships hidden in the reality

Authors: Martin Maria Kovár

Abstract
In most applications of general topology, topology usually is not the first, primary structure, but the information which finally leads to the construction of the certain, for some purpose required topology, is filtered by more or less thick filter of the other mathematical structures. This fact has two main consequences: (1) Most important applied constructions may be done in the primary structure, bypassing the topology. (2) Some topologically important information from the reality may be lost (filtered out by the other, front-end mathematical structures). Thus some natural and direct connection between topology and the reality could be useful. In this contribution we will discuss a pointless topological structure which directly reflects relationship between various locations which are glued together by possible presence of a physical object or a virtual ``observer".
Cite as

Martin Maria Kovár. Instant topological relationships hidden in the reality. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{kovar:DagSemProc.06341.6,
  author =	{Kov\'{a}r, Martin Maria},
  title =	{{Instant topological relationships hidden in the reality}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.6},
  URN =		{urn:nbn:de:0030-drops-8962},
  doi =		{10.4230/DagSemProc.06341.6},
  annote =	{Keywords: Pointless topology, reality}
}

Filters

  • Authors
  • B
  • Battenfeld, Ingo
  • Blair, Howard
  • K
  • Kopperman, Ralph
  • Kovár, Martin Maria
  • P
  • Panangaden, Prakash
  • Pfaltz, John L.
  • Porter, Timothy
  • S
  • Schröder, Matthias
  • Simpson, Alex
  • Smyth, Michael B.
  • Spreen, Dieter

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