eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2007-01-31
6391
1
21
10.4230/DagSemProc.06391.1
article
06391 Abstracts Collection – Algorithms and Complexity for Continuous Problems
Dahlke, Stephan
Ritter, Klaus
Sloan, Ian H.
Traub, Joseph F.
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol06391/DagSemProc.06391.1/DagSemProc.06391.1.pdf
Computational complexity
partial information
high-dimensional problems
operator equations
non-linear approximation
quantum computation
stochastic computation
ill posed-problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2007-01-31
6391
1
20
10.4230/DagSemProc.06391.2
article
Real Computational Universality: The Word Problem for a class of groups with infinite presentation
Meer, Klaus
Ziegler, Martin
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol06391/DagSemProc.06391.2/DagSemProc.06391.2.pdf
Computational group theory
word problem
Blum-Shub-Smale model
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2007-01-31
6391
1
25
10.4230/DagSemProc.06391.3
article
Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries
Barnum, Howard
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol06391/DagSemProc.06391.3/DagSemProc.06391.3.pdf
Quantum query complexity semidefinite programming