22,247 research outputs found
High-Level Methods for Quantum Computation and Information
A research programme is set out for developing the use of high-level methods
for quantum computation and information, based on the categorical formulation
of quantum mechanics introduced by the author and Bob Coecke.Comment: 5 page
Multidimensional hyperbolic billiards
The theory of planar hyperbolic billiards is already quite well developed by
having also achieved spectacular successes. In addition there also exists an
excellent monograph by Chernov and Markarian on the topic. In contrast, apart
from a series of works culminating in Sim\'anyi's remarkable result on the
ergodicity of hard ball systems and other sporadic successes, the theory of
hyperbolic billiards in dimension 3 or more is much less understood. The goal
of this work is to survey the key results of their theory and highlight some
central problems which deserve particular attention and efforts
Algebraic foundations for qualitative calculi and networks
A qualitative representation is like an ordinary representation of a
relation algebra, but instead of requiring , as
we do for ordinary representations, we only require that , for each in the algebra. A constraint
network is qualitatively satisfiable if its nodes can be mapped to elements of
a qualitative representation, preserving the constraints. If a constraint
network is satisfiable then it is clearly qualitatively satisfiable, but the
converse can fail. However, for a wide range of relation algebras including the
point algebra, the Allen Interval Algebra, RCC8 and many others, a network is
satisfiable if and only if it is qualitatively satisfiable.
Unlike ordinary composition, the weak composition arising from qualitative
representations need not be associative, so we can generalise by considering
network satisfaction problems over non-associative algebras. We prove that
computationally, qualitative representations have many advantages over ordinary
representations: whereas many finite relation algebras have only infinite
representations, every finite qualitatively representable algebra has a finite
qualitative representation; the representability problem for (the atom
structures of) finite non-associative algebras is NP-complete; the network
satisfaction problem over a finite qualitatively representable algebra is
always in NP; the validity of equations over qualitative representations is
co-NP-complete. On the other hand we prove that there is no finite
axiomatisation of the class of qualitatively representable algebras.Comment: 22 page
Symbolic Quantitative Information Flow
acmid: 2382791 issue_date: November 2012 keywords: algorithms, security, verification numpages: 5acmid: 2382791 issue_date: November 2012 keywords: algorithms, security, verification numpages: 5acmid: 2382791 issue_date: November 2012 keywords: algorithms, security, verification numpages: 5acmid: 2382791 issue_date: November 2012 keywords: algorithms, security, verification numpages: 5acmid: 2382791 issue_date: November 2012 keywords: algorithms, security, verification numpages:
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