587 research outputs found
The "paradox" of computability and a recursive relative version of the Busy Beaver function
In this article, we will show that uncomputability is a relative property not
only of oracle Turing machines, but also of subrecursive classes. We will
define the concept of a Turing submachine, and a recursive relative version for
the Busy Beaver function which we will call Busy Beaver Plus function.
Therefore, we will prove that the computable Busy Beaver Plus function defined
on any Turing submachine is not computable by any program running on this
submachine. We will thereby demonstrate the existence of a "paradox" of
computability a la Skolem: a function is computable when "seen from the
outside" the subsystem, but uncomputable when "seen from within" the same
subsystem. Finally, we will raise the possibility of defining universal
submachines, and a hierarchy of negative Turing degrees.Comment: 10 pages. 0 figures. Supported by the National Council for Scientific
and Technological Development (CNPq), Brazil. Book chapter published in
Information and Complexity, Mark Burgin and Cristian S. Calude (Editors),
World Scientific Publishing, 2016, ISBN 978-981-3109-02-5, available at
http://www.worldscientific.com/worldscibooks/10.1142/10017. arXiv admin note:
substantial text overlap with arXiv:1612.0522
Algorithmic information and incompressibility of families of multidimensional networks
This article presents a theoretical investigation of string-based generalized
representations of families of finite networks in a multidimensional space.
First, we study the recursive labeling of networks with (finite) arbitrary node
dimensions (or aspects), such as time instants or layers. In particular, we
study these networks that are formalized in the form of multiaspect graphs. We
show that, unlike classical graphs, the algorithmic information of a
multidimensional network is not in general dominated by the algorithmic
information of the binary sequence that determines the presence or absence of
edges. This universal algorithmic approach sets limitations and conditions for
irreducible information content analysis in comparing networks with a large
number of dimensions, such as multilayer networks. Nevertheless, we show that
there are particular cases of infinite nesting families of finite
multidimensional networks with a unified recursive labeling such that each
member of these families is incompressible. From these results, we study
network topological properties and equivalences in irreducible information
content of multidimensional networks in comparison to their isomorphic
classical graph.Comment: Extended preprint version of the pape
Nomic realism, simplicity, and the simplicity bubble effect
We offer an argument against simplicity as a sole intrinsic criterion for
nomic realism. The argument is based on the simplicity bubble effect.
Underdetermination in quantum foundations illustrates the case.Comment: Contributed talk for the Third Graduate Conference of the Italian
Network for the Philosophy of Mathematics --- FilMat. Submitted: September
15, 2023. Approved: October 25, 202
Emergence and algorithmic information dynamics of systems and observers
Previous work has shown that perturbation analysis in software space can
produce candidate computable generative models and uncover possible causal
properties from the finite description of an object or system quantifying the
algorithmic contribution of each of its elements relative to the whole. One of
the challenges for defining emergence is that one observer's prior knowledge
may cause a phenomenon to present itself to such observer as emergent while for
another as reducible. When attempting to quantify emergence, we demonstrate
that the methods of Algorithmic Information Dynamics can deal with the richness
of such observer-object dependencies both in theory and practice. By
formalising the act of observing as mutual algorithmic perturbation, the
emergence of algorithmic information is rendered invariant, minimal, and robust
in the face of information cost and distortion, while still observer-dependent.
We demonstrate that the unbounded increase of emergent algorithmic information
implies asymptotically observer-independent emergence, which eventually
overcomes any formal theory that an observer might devise to finitely
characterise a phenomenon. We discuss observer-dependent emergence and
asymptotically observer-independent emergence solving some previous suggestions
indicating a hard distinction between strong and weak emergence
Optimal Spatial Deconvolution and Message Reconstruction from a Large Generative Model of Models
We introduce a general-purpose univariate signal deconvolution method based
on the principles of an approach to Artificial General Intelligence. This
approach is based on a generative model that combines information theory and
algorithmic probability that required a large calculation of an estimation of a
`universal distribution' to build a general-purpose model of models independent
of probability distributions. This was used to investigate how non-random data
may encode information about the physical properties such as dimension and
length scales in which a signal or message may have been originally encoded,
embedded, or generated. This multidimensional space reconstruction method is
based on information theory and algorithmic probability, and it is agnostic,
but not independent, with respect to the chosen computable or semi-computable
approximation method or encoding-decoding scheme. The results presented in this
paper are useful for applications in coding theory, particularly in
zero-knowledge one-way communication channels, such as in deciphering messages
sent by generating sources of unknown nature for which no prior knowledge is
available. We argue that this can have strong potential for cryptography,
signal processing, causal deconvolution, life, and techno signature detection.Comment: 35 page
An algorithmically random family of MultiAspect Graphs and its topological properties
This article presents a theoretical investigation of incompressibility and randomness in generalized representations of graphs along with its implications on network topological properties. We extend previous studies on plain algorithmically random classical graphs to plain and prefix algorithmically random MultiAspect Graphs (MAGs). First, we show that there is an infinite recursively labeled infinite family of nested MAGs (or, as a particular case, of nested classical graphs) that behaves like (and is determined by) an algorithmically random real number. Then, we study some of their important topological properties, in particular, vertex degree, connectivity, diameter, and rigidity
Pragmatic Nonsense
Inspired by the early Wittgenstein's concept of nonsense (meaning that which
lies beyond the limits of language), we define two different, yet
complementary, types of nonsense: formal nonsense and pragmatic nonsense. The
simpler notion of formal nonsense is initially defined within Tarski's semantic
theory of truth; the notion of pragmatic nonsense, by its turn, is formulated
within the context of the theory of pragmatic truth, also known as quasi-truth,
as formalized by da Costa and his collaborators. While an expression will be
considered formally nonsensical if the formal criteria required for the
assignment of any truth-value (whether true, false, pragmatically true, or
pragmatically false) to such sentence are not met, a (well-formed) formula will
be considered pragmatically nonsensical if the pragmatic criteria (inscribed
within the context of scientific practice) required for the assignment of any
truth-value to such sentence are not met. Thus, in the context of the theory of
pragmatic truth, any (well-formed) formula of a formal language interpreted on
a simple pragmatic structure will be considered pragmatically nonsensical if
the set of primary sentences of such structure is not well-built, that is, if
it does not include the relevant observational data and/or theoretical results,
or if it does include sentences that are inconsistent with such data
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