14 Search Results for "Panangaden, Prakash"


Document
Tensor of Quantitative Equational Theories

Authors: Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin

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


Abstract
We develop a theory for the commutative combination of quantitative effects, their tensor, given as a combination of quantitative equational theories that imposes mutual commutation of the operations from each theory. As such, it extends the sum of two theories, which is just their unrestrained combination. Tensors of theories arise in several contexts; in particular, in the semantics of programming languages, the monad transformer for global state is given by a tensor. We show that under certain assumptions on the quantitative theories the free monad that arises from the tensor of two theories is the categorical tensor of the free monads on the theories. As an application, we provide the first algebraic axiomatizations of labelled Markov processes and Markov decision processes. Apart from the intrinsic interest in the axiomatizations, it is pleasing they are obtained compositionally by means of the sum and tensor of simpler quantitative equational theories.

Cite as

Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin. Tensor of Quantitative Equational Theories. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{bacci_et_al:LIPIcs.CALCO.2021.7,
  author =	{Bacci, Giorgio and Mardare, Radu and Panangaden, Prakash and Plotkin, Gordon},
  title =	{{Tensor of Quantitative Equational Theories}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{7:1--7:17},
  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.2021.7},
  URN =		{urn:nbn:de:0030-drops-153628},
  doi =		{10.4230/LIPIcs.CALCO.2021.7},
  annote =	{Keywords: Quantitative equational theories, Tensor, Monads, Quantitative Effects}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata

Authors: Borja Balle, Clara Lacroce, Prakash Panangaden, Doina Precup, and Guillaume Rabusseau

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
We address the approximate minimization problem for weighted finite automata (WFAs) with weights in ℝ, over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This work is grounded in Adamyan-Arov-Krein approximation theory, a remarkable collection of results on the approximation of Hankel operators. In addition to its intrinsic mathematical relevance, this theory has proven to be very effective for model reduction. We adapt these results to the framework of weighted automata over a one-letter alphabet. We provide theoretical guarantees and bounds on the quality of the approximation in the spectral and 𝓁² norm. We develop an algorithm that, based on the properties of Hankel operators, returns the optimal approximation in the spectral norm.

Cite as

Borja Balle, Clara Lacroce, Prakash Panangaden, Doina Precup, and Guillaume Rabusseau. Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 118:1-118:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{balle_et_al:LIPIcs.ICALP.2021.118,
  author =	{Balle, Borja and Lacroce, Clara and Panangaden, Prakash and Precup, Doina and Rabusseau, Guillaume},
  title =	{{Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{118:1--118:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.118},
  URN =		{urn:nbn:de:0030-drops-141873},
  doi =		{10.4230/LIPIcs.ICALP.2021.118},
  annote =	{Keywords: Weighted finite automata, approximate minimization, Hankel matrices, AAK Theory}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The Strahler Number of a Parity Game

Authors: Laure Daviaud, Marcin Jurdziński, and K. S. Thejaswini

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


Abstract
The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. It is proved that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices n and linear in (d/(2k))^k, where d is the number of priorities and k is the Strahler number. This complexity is quasi-polynomial because the Strahler number is at most logarithmic in the number of vertices. The proof is based on a new construction of small Strahler-universal trees. It is shown that the Strahler number of a parity game is a robust, and hence arguably natural, parameter: it coincides with its alternative version based on trees of progress measures and - remarkably - with the register number defined by Lehtinen (2018). It follows that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices and linear in (d/(2k))^k, where k is the register number. This significantly improves the running times and space achieved for parity games of bounded register number by Lehtinen (2018) and by Parys (2020). The running time of the algorithm based on small Strahler-universal trees yields a novel trade-off k ⋅ lg(d/k) = O(log n) between the two natural parameters that measure the structural complexity of a parity game, which allows solving parity games in polynomial time. This includes as special cases the asymptotic settings of those parameters covered by the results of Calude, Jain Khoussainov, Li, and Stephan (2017), of Jurdziński and Lazić (2017), and of Lehtinen (2018), and it significantly extends the range of such settings, for example to d = 2^O(√{lg n}) and k = O(√{lg n}).

Cite as

Laure Daviaud, Marcin Jurdziński, and K. S. Thejaswini. The Strahler Number of a Parity Game. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 123:1-123:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{daviaud_et_al:LIPIcs.ICALP.2020.123,
  author =	{Daviaud, Laure and Jurdzi\'{n}ski, Marcin and Thejaswini, K. S.},
  title =	{{The Strahler Number of a Parity Game}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{123:1--123:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.123},
  URN =		{urn:nbn:de:0030-drops-125304},
  doi =		{10.4230/LIPIcs.ICALP.2020.123},
  annote =	{Keywords: parity game, attractor decomposition, progress measure, universal tree, Strahler number}
}
Document
Bisimulation Metrics for Weighted Automata

Authors: Borja Balle, Pascale Gourdeau, and Prakash Panangaden

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale's linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of WFA plays a central role. We also study continuity properties of the bisimulation pseudometric, establish an undecidability result for computing the metric, and give a preliminary account of applications to spectral learning of weighted automata.

Cite as

Borja Balle, Pascale Gourdeau, and Prakash Panangaden. Bisimulation Metrics for Weighted Automata. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 103:1-103:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{balle_et_al:LIPIcs.ICALP.2017.103,
  author =	{Balle, Borja and Gourdeau, Pascale and Panangaden, Prakash},
  title =	{{Bisimulation Metrics for Weighted Automata}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{103:1--103:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.103},
  URN =		{urn:nbn:de:0030-drops-73959},
  doi =		{10.4230/LIPIcs.ICALP.2017.103},
  annote =	{Keywords: weighted automata, bisimulation, metrics, spectral theory, learning}
}
Document
Expressiveness of Probabilistic Modal Logics, Revisited

Authors: Nathanaël Fijalkow, Bartek Klin, and Prakash Panangaden

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. Logical characterizations of probabilistic bisimulation and simulation were given by Desharnais et al. These results hold for systems defined on analytic state spaces and assume that there are countably many labels in the case of bisimulation and finitely many labels in the case of simulation. In this paper, we first revisit these results by giving simpler and more streamlined proofs. In particular, our proof for simulation has the same structure as the one for bisimulation, relying on a new result of a topological nature. This departs from the known proof for this result, which uses domain theory techniques and falls out of a theory of approximation of Labelled Markov processes. Both our proofs assume the presence of countably many labels. We investigate the necessity of this assumption, and show that the logical characterization of bisimulation may fail when there are uncountably many labels. However, with a stronger assumption on the transition functions (continuity instead of just measurability), we can regain the logical characterization result, for arbitrarily many labels. These new results arose from a new game-theoretic way of understanding probabilistic simulation and bisimulation.

Cite as

Nathanaël Fijalkow, Bartek Klin, and Prakash Panangaden. Expressiveness of Probabilistic Modal Logics, Revisited. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 105:1-105:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{fijalkow_et_al:LIPIcs.ICALP.2017.105,
  author =	{Fijalkow, Nathana\"{e}l and Klin, Bartek and Panangaden, Prakash},
  title =	{{Expressiveness of Probabilistic Modal Logics, Revisited}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{105:1--105:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.105},
  URN =		{urn:nbn:de:0030-drops-73683},
  doi =		{10.4230/LIPIcs.ICALP.2017.105},
  annote =	{Keywords: probabilistic modal logic, probabilistic bisimulation, probabilistic simulation}
}
Document
06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality

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

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


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.

Cite as

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-dev.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
A convenient category of domains

Authors: Ingo Battenfeld, Matthias Schröder, and Alex Simpson

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


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.

Cite as

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-dev.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
Closure and Causality

Authors: John L. Pfaltz

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


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.

Cite as

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-dev.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
Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces

Authors: Howard Blair

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


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-dev.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
Enriched categories and models for spaces of dipaths

Authors: Timothy Porter

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


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-dev.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
Instant topological relationships hidden in the reality

Authors: Martin Maria Kovár

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


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-dev.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}
}
Document
04351 Abstracts Collection – Spatial Representation: Discrete vs. Continuous Computational Models

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

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
From 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351 ``Spatial Representation: Discrete vs. Continuous Computational Models'' 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.

Cite as

Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, Dieter Spreen, and Julian Webster. 04351 Abstracts Collection – Spatial Representation: Discrete vs. Continuous Computational Models. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{kopperman_et_al:DagSemProc.04351.1,
  author =	{Kopperman, Ralph and Panangaden, Prakash and Smyth, Michael B. and Spreen, Dieter and Webster, Julian},
  title =	{{04351 Abstracts Collection – Spatial Representation: Discrete vs. Continuous Computational Models}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--24},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.1},
  URN =		{urn:nbn:de:0030-drops-1742},
  doi =		{10.4230/DagSemProc.04351.1},
  annote =	{Keywords: Domain theory , formal topology , constructive topology , domain representation, space-time , quantum gravity , inverse limit construction, matroid geometry , descriptive set theory , Borel hierarchy , Hausdorff difference hierarchy , Wadge degree partial metric , fractafold , region geometry , oriented projective geometry}
}
Document
A domain of spacetime intervals in general relativity

Authors: Keye Martin and Prakash Panangaden

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This implies that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emanates from something discrete.

Cite as

Keye Martin and Prakash Panangaden. A domain of spacetime intervals in general relativity. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{martin_et_al:DagSemProc.04351.5,
  author =	{Martin, Keye and Panangaden, Prakash},
  title =	{{A domain of spacetime intervals in general relativity}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.5},
  URN =		{urn:nbn:de:0030-drops-1350},
  doi =		{10.4230/DagSemProc.04351.5},
  annote =	{Keywords: Causality , spacetime , global hyperbolicity , interval domains , bicontinuous posets , spacetime topology}
}
Document
04351 Summary – Spatial Representation: Discrete vs. Continuous Computational Models

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

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
Topological notions and methods are used in various areas of the physical sciences and engineering, and therefore computer processing of topological data is important. Separate from this, but closely related, are computer science uses of topology: applications to programming language semantics and computing with exact real numbers are important examples. The seminar concentrated on an important approach, which is basic to all these applications, i.e. spatial representation.

Cite as

Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, Dieter Spreen, and Julian Webster. 04351 Summary – Spatial Representation: Discrete vs. Continuous Computational Models. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{kopperman_et_al:DagSemProc.04351.2,
  author =	{Kopperman, Ralph and Panangaden, Prakash and Smyth, Michael B. and Spreen, Dieter and Webster, Julian},
  title =	{{04351 Summary – Spatial Representation: Discrete vs. Continuous Computational Models}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.2},
  URN =		{urn:nbn:de:0030-drops-1710},
  doi =		{10.4230/DagSemProc.04351.2},
  annote =	{Keywords: Domain theory , formal topology , constructive topology , domain representation , space-time , quantum gravity , inverse limit construction , matroid geometry , descriptive set theory , Borel hierarchy , Hausdorff difference hierarchy , Wadge degree , partial metric , fractafold , region geometry}
}
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