21,068 research outputs found
Duality of privacy amplification against quantum adversaries and data compression with quantum side information
We show that the tasks of privacy amplification against quantum adversaries
and data compression with quantum side information are dual in the sense that
the ability to perform one implies the ability to perform the other. These are
two of the most important primitives in classical information theory, and are
shown to be connected by complementarity and the uncertainty principle in the
quantum setting. Applications include a new uncertainty principle formulated in
terms of smooth min- and max-entropies, as well as new conditions for
approximate quantum error correction.Comment: v2: Includes a derivation of an entropic uncertainty principle for
smooth min- and max-entropies. Discussion of the
Holevo-Schumacher-Westmoreland theorem remove
An implementation of Deflate in Coq
The widely-used compression format "Deflate" is defined in RFC 1951 and is
based on prefix-free codings and backreferences. There are unclear points about
the way these codings are specified, and several sources for confusion in the
standard. We tried to fix this problem by giving a rigorous mathematical
specification, which we formalized in Coq. We produced a verified
implementation in Coq which achieves competitive performance on inputs of
several megabytes. In this paper we present the several parts of our
implementation: a fully verified implementation of canonical prefix-free
codings, which can be used in other compression formats as well, and an elegant
formalism for specifying sophisticated formats, which we used to implement both
a compression and decompression algorithm in Coq which we formally prove
inverse to each other -- the first time this has been achieved to our
knowledge. The compatibility to other Deflate implementations can be shown
empirically. We furthermore discuss some of the difficulties, specifically
regarding memory and runtime requirements, and our approaches to overcome them
Active Virtual Network Management Prediction: Complexity as a Framework for Prediction, Optimization, and Assurance
Research into active networking has provided the incentive to re-visit what
has traditionally been classified as distinct properties and characteristics of
information transfer such as protocol versus service; at a more fundamental
level this paper considers the blending of computation and communication by
means of complexity. The specific service examined in this paper is network
self-prediction enabled by Active Virtual Network Management Prediction.
Computation/communication is analyzed via Kolmogorov Complexity. The result is
a mechanism to understand and improve the performance of active networking and
Active Virtual Network Management Prediction in particular. The Active Virtual
Network Management Prediction mechanism allows information, in various states
of algorithmic and static form, to be transported in the service of prediction
for network management. The results are generally applicable to algorithmic
transmission of information. Kolmogorov Complexity is used and experimentally
validated as a theory describing the relationship among algorithmic
compression, complexity, and prediction accuracy within an active network.
Finally, the paper concludes with a complexity-based framework for Information
Assurance that attempts to take a holistic view of vulnerability analysis
Shannon Information and Kolmogorov Complexity
We compare the elementary theories of Shannon information and Kolmogorov
complexity, the extent to which they have a common purpose, and where they are
fundamentally different. We discuss and relate the basic notions of both
theories: Shannon entropy versus Kolmogorov complexity, the relation of both to
universal coding, Shannon mutual information versus Kolmogorov (`algorithmic')
mutual information, probabilistic sufficient statistic versus algorithmic
sufficient statistic (related to lossy compression in the Shannon theory versus
meaningful information in the Kolmogorov theory), and rate distortion theory
versus Kolmogorov's structure function. Part of the material has appeared in
print before, scattered through various publications, but this is the first
comprehensive systematic comparison. The last mentioned relations are new.Comment: Survey, LaTeX 54 pages, 3 figures, Submitted to IEEE Trans
Information Theor
Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes
I argue that data becomes temporarily interesting by itself to some
self-improving, but computationally limited, subjective observer once he learns
to predict or compress the data in a better way, thus making it subjectively
simpler and more beautiful. Curiosity is the desire to create or discover more
non-random, non-arbitrary, regular data that is novel and surprising not in the
traditional sense of Boltzmann and Shannon but in the sense that it allows for
compression progress because its regularity was not yet known. This drive
maximizes interestingness, the first derivative of subjective beauty or
compressibility, that is, the steepness of the learning curve. It motivates
exploring infants, pure mathematicians, composers, artists, dancers, comedians,
yourself, and (since 1990) artificial systems.Comment: 35 pages, 3 figures, based on KES 2008 keynote and ALT 2007 / DS 2007
joint invited lectur
- …