arXiv subjects

Hector Zenil

Publications and source records attributed to Hector Zenil.

At least 109 records · Page 6Linked to original sources

arXiv2014

Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks

We show that numerical approximations of Kolmogorov complexity (K) applied to graph adjacency matrices capture some group-theoretic and topological properties of graphs and empirical networks ranging from metabolic to social networks. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We show that approximations of K characterise synthetic and natural networks by their generating mechanisms, assigning lower algorithmic randomness to complex network models (Watts-Strogatz and Barabasi-Albert networks) and high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and a normalised version of a Block Decomposition Method (BDM) measure, based on algorithmic probability theory.

cs.IT↗

arXiv2014

Levels of Abstraction and the Apparent Contradictory Philosophical Legacy of Turing and Shannon

In a recent article, Luciano Floridi explains his view of Turing's legacy in connection to the philosophy of information. I will very briefly survey one of Turing's other contributions to the philosophy of information and computation, including similarities to Shannon's own methodological approach to information through communication, showing how crucial they are and have been as methodological strategies to understanding key aspects of these concepts. While Floridi's concept of Levels of Abstraction is related to the novel methodology of Turing's imitation game for tackling the question of machine intelligence, Turing's other main contribution to the philosophy of information runs contrary to it. Indeed, the seminal concept of computation universality strongly suggests the deletion of fundamental differences among seemingly different levels of description. How might we reconcile these apparently contradictory contributions? I will argue that Turing's contribution should prompt us to plot some directions for a philosophy of information and computation, one that closely parallels the most important developments in computer science, one that understands the profound implications of the works of Turing, Shannon and others.

cs.GL↗

arXiv2013

Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them focuses on one feature of randomness, leading authors to have to use multiple measures. Here we describe and advocate for the use of the accepted universal measure for randomness based on algorithmic complexity, by means of a novel previously presented technique using the the definition of algorithmic probability. A re-analysis of the classical Radio Zenith data in the light of the proposed measure and methodology is provided as a study case of an application.

cs.CC↗

arXiv2013

Exploring Programmable Self-Assembly in Non-DNA based Molecular Computing

Self-assembly is a phenomenon observed in nature at all scales where autonomous entities build complex structures, without external influences nor centralised master plan. Modelling such entities and programming correct interactions among them is crucial for controlling the manufacture of desired complex structures at the molecular and supramolecular scale. This work focuses on a programmability model for non DNA-based molecules and complex behaviour analysis of their self-assembled conformations. In particular, we look into modelling, programming and simulation of porphyrin molecules self-assembly and apply Kolgomorov complexity-based techniques to classify and assess simulation results in terms of information content. The analysis focuses on phase transition, clustering, variability and parameter discovery which as a whole pave the way to the notion of complex systems programmability.

cs.CC↗

arXiv2013

Computation and Universality: Class IV versus Class III Cellular Automata

This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the course of the CA history, that may be candidates for universal computation, hence spurring the discussion on Turing universality on both Wolfram's classes III and IV.

nlin.CG↗

arXiv2013

Correspondence and Independence of Numerical Evaluations of Algorithmic Information Measures

We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols), is in agreement with the number of instructions used by the Turing machines producing s, which is consistent with strict integer-value program-size complexity. Nevertheless, K_m proves to be a finer-grained measure and a potential alternative approach to lossless compression algorithms for small entities, where compression fails. We also show that neither K_m nor the number of instructions used shows any correlation with Bennett's Logical Depth LD(s) other than what's predicted by the theory. The agreement between theory and numerical calculations shows that despite the undecidability of these theoretical measures, approximations are stable and meaningful, even for small programs and for short strings. We also announce a first Beta version of an Online Algorithmic Complexity Calculator (OACC), based on a combination of theoretical concepts, as a numerical implementation of the Coding Theorem Method.

cs.IT↗

arXiv2012

What is Nature-like Computation? A Behavioural Approach and a Notion of Programmability

The aim of this paper is to propose an alternative behavioural definition of computation (and of a computer) based simply on whether a system is capable of reacting to the environment-the input-as reflected in a measure of programmability. This definition is intended to have relevance beyond the realm of digital computers, particularly vis-a-vis natural systems. This will be done by using an extension of a phase transition coefficient previously defined in an attempt to characterise the dynamical behaviour of cellular automata and other systems. The transition coefficient measures the sensitivity of a system to external stimuli, and will be used to define the susceptibility of a system to being (efficiently) programmed.

cs.LO↗

arXiv2012

Turing Patterns with Turing Machines: Emergence and Low-level Structure Formation

Despite having advanced a reaction-diffusion model of ODE's in his 1952 paper on morphogenesis, reflecting his interest in mathematical biology, Alan Turing has never been considered to have approached a definition of Cellular Automata. However, his treatment of morphogenesis, and in particular a difficulty he identified relating to the uneven distribution of certain forms as a result of symmetry breaking, are key to connecting his theory of universal computation with his theory of biological pattern formation. Making such a connection would not overcome the particular difficulty that Turing was concerned about, which has in any case been resolved in biology. But instead the approach developed here captures Turing's initial concern and provides a low-level solution to a more general question by way of the concept of algorithmic probability, thus bridging two of his most important contributions to science: Turing pattern formation and universal computation. I will provide experimental results of one-dimensional patterns using this approach, with no loss of generality to a n-dimensional pattern generalisation.

cs.CC↗

arXiv2012

Wolfram's Classification and Computation in Cellular Automata Classes III and IV

We conduct a brief survey on Wolfram's classification, in particular related to the computing capabilities of Cellular Automata (CA) in Wolfram's classes III and IV. We formulate and shed light on the question of whether Class III systems are capable of Turing universality or may turn out to be "too hot" in practice to be controlled and programmed. We show that systems in Class III are indeed capable of computation and that there is no reason to believe that they are unable, in principle, to reach Turing-completness.

nlin.CG↗

arXiv2012

Some Computational Aspects of Essential Properties of Evolution and Life

While evolution has inspired algorithmic methods of heuristic optimisation, little has been done in the way of using concepts of computation to advance our understanding of salient aspects of biological phenomena. We argue that under reasonable assumptions, interesting conclusions can be drawn that are of relevance to behavioural evolution. We will focus on two important features of life--robustness and fitness--which, we will argue, are related to algorithmic probability and to the thermodynamics of computation, disciplines that may be capable of modelling key features of living organisms, and which can be used in formulating new algorithms of evolutionary computation.

cs.CC↗

arXiv2012

Introducing the Computable Universe

Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic arguments giving foundation to these visions. We will focus on the algorithmic and quantum aspects, and how these may fit and support the computable universe hypothesis.

cs.IT↗

arXiv2012

Très courte enquête sur l'extension non-triviale de la logique de propositions à la logique du premier et deuxième ordre

The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are of higher-order? What type of order matches the natural language? Is there a philosophical position behind every logic, even for classical ones? What philosophical position for what logic in connection to its expressive power? These are the questions we ask and that we very briefly sketch as a first reflection. (paper in French)

math.LO↗

arXiv2012

On the Dynamic Qualitative Behaviour of Universal Computation

We explore the possible connections between the dynamic behaviour of a system and Turing universality in terms of the system's ability to (effectively) transmit and manipulate information. Some arguments will be provided using a defined compression-based transition coefficient which quantifies the sensitivity of a system to being programmed. In the same spirit, a list of conjectures concerning the ability of Busy Beaver Turing machines to perform universal computation will be formulated. The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulus--as it needs to be programmed--and to its capacity for transmitting this information.

cs.CC↗

arXiv2012

Computer Runtimes and the Length of Proofs: On an Algorithmic Probabilistic Application to Waiting Times in Automatic Theorem Proving

This paper is an experimental exploration of the relationship between the runtimes of Turing machines and the length of proofs in formal axiomatic systems. We compare the number of halting Turing machines of a given size to the number of provable theorems of first-order logic of a given size, and the runtime of the longest-running Turing machine of a given size to the proof length of the most-difficult-to-prove theorem of a given size. It is suggested that theorem provers are subject to the same non-linear tradeoff between time and size as computer programs are, affording the possibility of determining optimal timeouts and waiting times in automatic theorem proving. I provide the statistics for some small choices of parameters for both of these systems.

cs.CC↗

arXiv2011

Numerical Evaluation of Algorithmic Complexity for Short Strings: A Glance into the Innermost Structure of Randomness

We describe an alternative method (to compression) that combines several theoretical and experimental results to numerically approximate the algorithmic (Kolmogorov-Chaitin) complexity of all $\sum_{n=1}^82^n$ bit strings up to 8 bits long, and for some between 9 and 16 bits long. This is done by an exhaustive execution of all deterministic 2-symbol Turing machines with up to 4 states for which the halting times are known thanks to the Busy Beaver problem, that is 11019960576 machines. An output frequency distribution is then computed, from which the algorithmic probability is calculated and the algorithmic complexity evaluated by way of the (Levin-Zvonkin-Chaitin) coding theorem.

cs.IT↗

arXiv2011

An Algorithmic Approach to Information and Meaning

I will survey some matters of relevance to a philosophical discussion of information, taking into account developments in algorithmic information theory (AIT). I will propose that meaning is deep in the sense of Bennett's logical depth, and that algorithmic probability may provide the stability needed for a robust algorithmic definition of meaning, one that takes into consideration the interpretation and the recipient's own knowledge encoded in the story attached to a message.

cs.IT↗

arXiv2011

The World is Either Algorithmic or Mostly Random

I will propose the notion that the universe is digital, not as a claim about what the universe is made of but rather about the way it unfolds. Central to the argument will be the concepts of symmetry breaking and algorithmic probability, which will be used as tools to compare the way patterns are distributed in our world to the way patterns are distributed in a simulated digital one. These concepts will provide a framework for a discussion of the informational nature of reality. I will argue that if the universe were analog, then the world would likely be random, making it largely incomprehensible. The digital model has, however, an inherent beauty in its imposition of an upper limit and in the convergence in computational power to a maximal level of sophistication. Even if deterministic, that it is digital doesn't mean that the world is trivial or predictable, but rather that it is built up from operations that at the lowest scale are very simple but that at a higher scale look complex and even random, though only in appearance.

cs.IT↗

arXiv2011

Un metodo estable para la evaluacion de la complejidad algoritmica de cadenas cortas

It is discussed and surveyed a numerical method proposed before, that alternative to the usual compression method, provides an approximation to the algorithmic (Kolmogorov) complexity, particularly useful for short strings for which compression methods simply fail. The method shows to be stable enough and useful to conceive and compare patterns in an algorithmic models. (article in Spanish)

cs.CC↗