Learning the undecidable from networked systems

We analyze a distributed information network in which each node has access to the information contained in a limited set of nodes (its neighborhood) at a given time. A collective computation is carried out in which each node calculates a value that implies all information contained in the network (in our case, the average value of a variable that can take different values in each network node). The neighborhoods can change dynamically by exchanging neighbors with other nodes. The results of this collective calculation show rapid convergence and good scalability with the network size. These results are compared with those of a fixed network arranged as a square lattice, in which the number of rounds to achieve a given accuracy is very high when the size of the network increases. The results for the evolving networks are interpreted in light of the properties of complex networks and are directly relevant to the diameter and characteristic path length of the networks, which seem to express "small world" properties.

Theory of Computing Systems, 2012

This special issue of Theory or Computing Systems consists of papers associated with the 6th Annual CCR conference held in beautiful Cape Town, 31st January-February 4th 2011. The conference series is devoted to issues around algorithmic information theory, Kolmogorov complexity, and their relationship with computability theory, complexity theory, logic and reverse mathematics. In 2011, the conference was co-located with the 8th Annual Computability and Analysis conference. This co-location reflects the increasing interactions between computable analysis and algorithmic randomness through effective analysis of almost everywhere behavior in analysis such as the Lebesgue Differentiation Theorem and things like Brownian motion. Both conferences were admirably overseen by Vasco Brattka and his program committees. The last 10-15 years has seen huge progress in the areas represented by CCR with two long monographs in the area, recognition at the International Congress of Mathematicians, and a thoroughly thriving research community. Whilst the CCR conference uses a model which does not have an actual proceedings at the meeting, the papers in this special issue reflect the meeting's business. These papers reflect the high caliber of both the researchers and the intellectual merit of the investigations. The work spans issues from applications in biology, computer science to fundamental issues about Kolmogorov complexity. The papers all went through the full Theory of Computing Systems journal reviewing process and several of the initial submissions were rejected. Enjoy.

Workshop on Distributed Algorithms/International Symposium on Distributed Computing, 2008

We investigate the computability of distributed tasks in re- liable anonymous networks with arbitrary knowledge. More precisely, we consider tasks computable with local termination, i.e., a node knows when to stop to participate in a distributed algorithm, even though the algorithm is not necessarily terminated elsewhere. We also study weak local termination, that is when a node knows its final

Big Data: implicações epistemológicas e éticas, 2020

As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological characteristics, such as the small-world phenomenon, small-diameter, scale-free properties, or fat-tailed degree distribution were one of the underlying pillars fostering the study of complex networks. Relating these phenomena with other emergent properties in complex systems became a subject of central importance. By introducing new implications on the interface between data science and complex systems science with the purpose of tackling some of these issues, in this article we present a model for a network game played by complex networks in which nodes are computable systems. In particular, we present and discuss how some network topological properties and simple local communication rules are able to generate a phase transition with respect to the emergence of incompressible data.

Physics of Life Reviews, 2019

In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of G¨odel’s proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of Godel’s proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.

Brazilian Computer Society Congress 2018 (CSBC 2018), 2018

We study emergent information in populations of randomly generated networked computable systems that follow a susceptible-infected-susceptible contagion (or infection) model of imitation of the fittest neighbor. These networks have a scale-free degree distribution in the form of a power-law following the Barabási-Albert model. We show that there is a lower bound for the stationary prevalence (or average density of infected nodes) that triggers an unlimited increase of the expected emergent algorithmic complexity (or information) of a node as the population size grows.

Foundations of Science, 2012

The aim of the paper is to introduce some of the history and key concepts of network science to a philosophical audience, and to highlight a crucial-and often problematic-presumption that underlies the network approach to complex systems. Network scientists often talk of "the structure" of a given complex system or phenomenon, which encourages the view that there is a unique and privileged structure inherent to the system, and that the aim of a network model is to delineate this structure. I argue that this sort of naïve realism about structure is not a coherent or plausible position, especially given the multiplicity of types of entities and relations that can feature as nodes and links in complex networks.

The British Journal for the Philosophy of Science

We consider how an epistemic network might self-assemble from the ritualization of the individual decisions of simple heterogeneous agents. In such evolved social networks, inquirers may be significantly more successful than they could be investigating nature on their own. The evolved network may also dramatically lower the epistemic risk faced by even the most talented inquirers. We consider networks that self-assemble in the context of both perfect and imperfect communication and compare the behavior of inquirers in each. This provides a step in bringing together two new and developing research programs, the theory of self-assembling games and the theory of network epistemology.

Complex Systems (ISSN 0891-2513), 2018

In this work, we study emergent information in populations of randomly generated computable systems that are networked and follow a " Susceptible-Infected-Susceptible " contagion model of imitation of the fittest neighbor. We show that there is a lower bound for the stationary prevalence (or average density of " infected " nodes) that triggers an unlimited increase of the expected local emergent algorithmic complexity (or information) of a node as the population size grows. A phenomenon we have called as expected (local) emergent open-endedness. In addition, we show that static networks with a scale-free degree distribution in the form of a power-law following the Barabási-Albert model satisfy this lower bound and, thus, displays expected (local) emergent open-endedness.

Ai Communications, 2002

The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such organisms. We describe a scenario in which an artificial living (AL) system is involved in a potentially infinite, unpredictable interaction with an active or passive environment, to which it can react by learning and adjusting its behaviour. By making use of sequences of cognitive transducers one can also model the evolution of AL systems caused by 'architectural' changes. Among the examples are 'communities of agents', i.e. by communities of mobile, interactive cognitive transducers. Most AL systems show the emergence of a computational power that is not present at the level of the individual organisms. Indeed, in all but trivial cases the resulting systems possess a super-Turing computing power. This means that the systems cannot be simulated by traditional computational models like Turing machines and may in principle solve noncomputable tasks. The results are derived using non-uniform complexity theory.