181,221 research outputs found
Algorithmic information theory
This article is a brief guide to the field of algorithmic information theory (AIT), its underlying philosophy, and the most important concepts. AIT arises by mixing information theory and computation theory to obtain an objective and absolute notion of information in an individual object, and in so doing gives rise to an objective and robust notion of randomness of individual objects. This is in contrast to classical information theory that is based on random variables and communication, and has no bearing on information and randomness of individual objects. After a brief overview, the major subfields, applications, history, and a map of the field are presented
Algorithmic Information Theory and Foundations of Probability
The use of algorithmic information theory (Kolmogorov complexity theory) to
explain the relation between mathematical probability theory and `real world'
is discussed
Quantum Kolmogorov Complexity and Quantum Key Distribution
We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol
in the light of quantum algorithmic information. While Shannon's information
theory needs a probability to define a notion of information, algorithmic
information theory does not need it and can assign a notion of information to
an individual object. The program length necessary to describe an object,
Kolmogorov complexity, plays the most fundamental role in the theory. In the
context of algorithmic information theory, we formulate a security criterion
for the quantum key distribution by using the quantum Kolmogorov complexity
that was recently defined by Vit\'anyi. We show that a simple BB84 protocol
indeed distribute a binary sequence between Alice and Bob that looks almost
random for Eve with a probability exponentially close to 1.Comment: typos correcte
Is Consciousness Computable? Quantifying Integrated Information Using Algorithmic Information Theory
In this article we review Tononi's (2008) theory of consciousness as
integrated information. We argue that previous formalizations of integrated
information (e.g. Griffith, 2014) depend on information loss. Since lossy
integration would necessitate continuous damage to existing memories, we
propose it is more natural to frame consciousness as a lossless integrative
process and provide a formalization of this idea using algorithmic information
theory. We prove that complete lossless integration requires noncomputable
functions. This result implies that if unitary consciousness exists, it cannot
be modelled computationally.Comment: Maguire, P., Moser, P., Maguire, R. & Griffith, V. (2014). Is
consciousness computable? Quantifying integrated information using
algorithmic information theory. In P. Bello, M. Guarini, M. McShane, & B.
Scassellati (Eds.), Proceedings of the 36th Annual Conference of the
Cognitive Science Society. Austin, TX: Cognitive Science Societ
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