Volume

Dagstuhl Seminar Proceedings, Volume 6391



Publication Details

  • published at: 2007-01-31
  • Publisher: Schloss-Dagstuhl - Leibniz Zentrum für Informatik

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Document
06391 Abstracts Collection – Algorithms and Complexity for Continuous Problems

Authors: Stephan Dahlke, Klaus Ritter, Ian H. Sloan, and Joseph F. Traub


Abstract
From 24.09.06 to 29.09.06, the Dagstuhl Seminar 06391 ``Algorithms and Complexity for Continuous Problems'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar 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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Stephan Dahlke, Klaus Ritter, Ian H. Sloan, and Joseph F. Traub. 06391 Abstracts Collection – Algorithms and Complexity for Continuous Problems. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 6391, pp. 1-21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)


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@InProceedings{dahlke_et_al:DagSemProc.06391.1,
  author =	{Dahlke, Stephan and Ritter, Klaus and Sloan, Ian H. and Traub, Joseph F.},
  title =	{{06391 Abstracts Collection – Algorithms and Complexity for Continuous Problems}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--21},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6391},
  editor =	{Stephan Dahlke and Klaus Ritter and Ian H. Sloan and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06391.1},
  URN =		{urn:nbn:de:0030-drops-8782},
  doi =		{10.4230/DagSemProc.06391.1},
  annote =	{Keywords: Computational complexity, partial information, high-dimensional problems, operator equations, non-linear approximation, quantum computation, stochastic computation, ill posed-problems}
}
Document
Real Computational Universality: The Word Problem for a class of groups with infinite presentation

Authors: Klaus Meer and Martin Ziegler


Abstract
In this talk we introduce a class of groups represented as quotient groups of some free groups generated by infinitely many elements and certain normal subgroups. We show that the related word problem is universal in the Blum-Shub-Smale model of computation, i.e. it has the same difficulty as the real Halting Problem. This is the first natural example of a problem with this property. The work has been done jointly with Martin Ziegler.

Cite as

Klaus Meer and Martin Ziegler. Real Computational Universality: The Word Problem for a class of groups with infinite presentation. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 6391, pp. 1-20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)


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@InProceedings{meer_et_al:DagSemProc.06391.2,
  author =	{Meer, Klaus and Ziegler, Martin},
  title =	{{Real Computational Universality: The Word Problem for a class of groups with infinite presentation}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6391},
  editor =	{Stephan Dahlke and Klaus Ritter and Ian H. Sloan and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06391.2},
  URN =		{urn:nbn:de:0030-drops-8773},
  doi =		{10.4230/DagSemProc.06391.2},
  annote =	{Keywords: Computational group theory, word problem, Blum-Shub-Smale model}
}
Document
Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries

Authors: Howard Barnum


Abstract
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model in which the goal is to compute functions of $N imes N$ ``black box'' unitary matrices drawn from a set of such matrices, a problem with applications to determining properties of quantum physical systems. We characterize the existence of an algorithm for such a query problem, with given query and error, as equivalent to the feasibility of a certain set of semidefinite programming constraints, or equivalently the infeasibility of a dual of these constraints, which we construct. Relaxing the primal constraints to correspond to mere pairwise near-orthogonality of the final states of a quantum computer, conditional on the various black-box inputs, rather than bounded-error distinguishability, we obtain a relaxed primal program the feasibility of whose dual still implies the nonexistence of a quantum algorithm. We use this to obtain a generalization, to our not-necessarily-commutative setting, of the ``spectral adversary method'' for quantum query lower bounds.

Cite as

Howard Barnum. Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 6391, pp. 1-25, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)


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@InProceedings{barnum:DagSemProc.06391.3,
  author =	{Barnum, Howard},
  title =	{{Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6391},
  editor =	{Stephan Dahlke and Klaus Ritter and Ian H. Sloan and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06391.3},
  URN =		{urn:nbn:de:0030-drops-8769},
  doi =		{10.4230/DagSemProc.06391.3},
  annote =	{Keywords: Quantum query complexity semidefinite programming}
}

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