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Generalized Convolution Roots of Positive Definite Kernels on Complex Spheres
Convolution is an important tool in the construction of positive definite
kernels on a manifold. This contribution provides conditions on an
-positive definite and zonal kernel on the unit sphere of
in order that the kernel can be recovered as a generalized convolution root of
an equally positive definite and zonal kernel
A logic for n-dimensional hierarchical refinement
Hierarchical transition systems provide a popular mathematical structure to
represent state-based software applications in which different layers of
abstraction are represented by inter-related state machines. The decomposition
of high level states into inner sub-states, and of their transitions into inner
sub-transitions is common refinement procedure adopted in a number of
specification formalisms.
This paper introduces a hybrid modal logic for k-layered transition systems,
its first-order standard translation, a notion of bisimulation, and a modal
invariance result. Layered and hierarchical notions of refinement are also
discussed in this setting.Comment: In Proceedings Refine'15, arXiv:1606.0134
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