Algorithmicity and programmability in natural computing with the Game of Life as in silico case study

In a previous article, I suggested a method for testing the algorithmicity of a natural/physical process using the concept of Levin’s universal distribution. In this new paper published by the Journal of Experimental & Theoretical Artificial Intelligence, I explain this method in the context of the problem formulated by Floridi concerning the testability of pancomputationalism. Then, I […]

How Humans perceive the world is biased by how patterns are distributed in Nature and their intrinsic complexity

A new paper of mine with my colleagues, and Algorithmic Nature Lab members, Nicolas Gauvrit and Fernando Soler-Toscano just came out. Using previously generated and new experimental data together with new methods to calculate the algorithmic complexity of 2-dimensional objects, we were able to find that when humans assess the complexity of an image (a small 4×4 […]

Calculating a Universal Distribution to Approximate Kolmogorov-Chaitin Complexity

Computing the incomputable has always been a challenge. For example, in finding the busiest Turing machines (Rado) given a number of symbols and states (whimsically called busy beavers). This means either finding Turing machines that, starting from an empty input, produce more non-blank symbols in their output tapes before halting than any other Turing machine […]

Conjectures concerning Busy Beavers, Dynamic Behavior and Turing Universality

In a recent paper I have advanced some conjectures using a coefficient that renders aspects of the qualitative behavior of complex systems in quantitative terms. It measures the sensitivity of a system to external stimuli, its apparent ability to (efficiently) transfer information from the input through the output. In a previous paper, and in a […]

Turing’s Deep Field: Visualizing the Computational Universe

I generated this image in the course of an investigation of the distribution of runtimes of programs in relation to the lengths of mathematical proofs, the results of which are being published in my paper bearing the title “Computer Runtimes and the Length of Proofs with an Algorithmic Probabilistic Application to Optimal Waiting Times in […]

Compression-based Investigation of Cellular Automata, A Phase Transition Coefficient and a Conjecture Related to Universal Computation

In a recent paper, forthcoming in the Journal of Complex Systems, vol. 19, I present a method for studying the qualitative behavior of cellular automata and other abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm. I show that the compression-based approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram’s main classes of systemic behavior. I also present a Gray code-based numbering scheme for initial conditions optimal for this kind of investigations, and a compression based method for estimating a characteristic exponent in the form of a phase transition coefficient measuring the resiliency or sensitivity of a system to its initial conditions. I also conjecture that universal systems have large transition coefficients.

Classifying objects by complexity

We present a method for estimating the complexity of an image based on the concept of Bennett’s logical depth. We use this measure to classify images by their information content. The method provides a means for evaluating and classifying objects by way of their visual representations.

Comments on Turing’s very first Universal machine approaching Turing’s 100th. birthday anniversary

The idea that a machine could perform the tasks of any other machine is the description of a Universal (Turing) machine. Its invention is considered by many to have been one of the major landmarks giving rise to the field of computer science. ‘Universal’ means that one can ‘program’ a general-purpose machine to perform the […]

On the Kolmogorov-Chaitin complexity for short sequences

My paper On the Kolmogorov-Chaitin complexity for short sequences, coauthored with my PhD thesis advisor Jean-Paul Delahaye has been published as a book chapter in:RANDOMNESS AND COMPLEXITY, FROM LEIBNIZ TO CHAITIN, edited by Cristian S. Calude (University of Auckland, New Zealand) and published by World Scientific. An extended draft version of this paper can be […]

On the simplest and smallest universal Turing machine

Alex Smith has recently been able to prove that a Turing machine conjectured to be capable of universal computation by Wolfram was actually universal (Wolfram 2,3 Turing machine Research Prize). Part of the challenge was to find an encoding not doing by itself the universal computation that would make the Turing machine universal. Smith succeeded […]

Meaning against A.I.

A significant number of researchers believe that there are sentences with semantic value that could never be understood by a machine. These researchers believe that the mind has a semantic component, unlike machines. Their’s is a  Chinese Room type argument a la Searle. Consider Chomsky’s example of two books in a library with the same title, and […]

Hacking Days at MIT and Wikimania at Harvard, August 2006.

Hacking Days at MIT and Wikimania at the Harvard Law School came to a close yesterday. Here is a brief summary: Brion Vibber, Chief Technology Officer of Wikimedia, gave many talks. He discussed everything from why wiki projects are difficult to cache (since they are dynamical) to new features to come, like Semantic MediaWiki, a possible Xapian search […]

Computability in Europe Conference (CiE) Report, Wales UK

This is a report on the Computability in Europe Conference (CiE), held at the University of Swansea, Wales in the United Kingdom in July 2006. I attended a mini-course on Quantum Computing given by Julia Kempe, a lecture on the Church-Turing thesis by Martin Davis– who defended it against proposed models of hypercomputation– and a  lecture on Proof […]

International Conference in Complex Systems, NECSI

NECSI/ICCS Conference Report, Quincy, Greater Boston, USA, July 2006. First lesson: For every complex problem there is a simple, neat, wrong solution. I attended talks given by Ed Fredkin on Finite Nature, Lazlo Barabasi on Complex Networks, Christoph Teuscher on Biology and Computation and John Nash on his research upon Game Theory. * Ed Fredkin presented […]

How To Criticize Computer Scientists

How To Criticize Computer Scientists or Avoiding Ineffective Deprecation And Making Insults More Pointed, from http://www.cs.purdue.edu/homes/dec/essay.criticize.html In recent exchanges, members of the faculty have tried in vain to attack other Computer Scientists and disparage their work. Quite frankly, I find the results embarrassing — instead of cutting the opponent down, many of the remarks have been […]