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	<title>Anima Ex Machina &#187; Computer Science</title>
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	<description>The blog of Hector Zenil</description>
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		<title>Turing&#8217;s Deep Field: Visualizing the Computational Universe</title>
		<link>http://www.mathrix.org/liquid/archives/visualizing-the-computational-universe-or-turings-deep-field</link>
		<comments>http://www.mathrix.org/liquid/archives/visualizing-the-computational-universe-or-turings-deep-field#comments</comments>
		<pubDate>Thu, 05 Jan 2012 06:41:14 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Complexity]]></category>
		<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[Foundations of Math]]></category>
		<category><![CDATA[Mathematical Logic]]></category>
		<category><![CDATA[automatic theorem proving]]></category>
		<category><![CDATA[busy beaver]]></category>
		<category><![CDATA[computer runtimes]]></category>
		<category><![CDATA[halting problem]]></category>
		<category><![CDATA[halting times]]></category>
		<category><![CDATA[length of proofs]]></category>
		<category><![CDATA[Turing machines]]></category>

		<guid isPermaLink="false">http://www.mathrix.org/liquid/?p=924</guid>
		<description><![CDATA[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 &#8220;Computer Runtimes and the Length of Proofs with an Algorithmic Probabilistic Application to Optimal Waiting Times in [...]]]></description>
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		<title>Compression-based Investigation of Cellular Automata, A Phase Transition Coefficient and a Conjecture Related to Universal Computation</title>
		<link>http://www.mathrix.org/liquid/archives/compression-based-investigation-of-the-dynamical-properties-of-cellular-automata-phase-transition-classification-and-a-universality-conjecture</link>
		<comments>http://www.mathrix.org/liquid/archives/compression-based-investigation-of-the-dynamical-properties-of-cellular-automata-phase-transition-classification-and-a-universality-conjecture#comments</comments>
		<pubDate>Sun, 22 Aug 2010 02:18:32 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Algorithmic information theory]]></category>
		<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[New Ideas]]></category>

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		<description><![CDATA[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.]]></description>
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		<slash:comments>3</slash:comments>
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		<title>Classifying objects by complexity</title>
		<link>http://www.mathrix.org/liquid/archives/classifying-objects-by-physical-complexity-via-their-images</link>
		<comments>http://www.mathrix.org/liquid/archives/classifying-objects-by-physical-complexity-via-their-images#comments</comments>
		<pubDate>Wed, 02 Jun 2010 01:35:21 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Algorithmic information theory]]></category>
		<category><![CDATA[Complexity]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[New Ideas]]></category>
		<category><![CDATA[algorithmic information theory]]></category>
		<category><![CDATA[Bennett's logical depth]]></category>
		<category><![CDATA[complexity]]></category>

		<guid isPermaLink="false">http://www.mathrix.org/liquid/?p=430</guid>
		<description><![CDATA[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.]]></description>
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		<title>Comments on Turing&#8217;s very first Universal machine approaching Turing&#8217;s 100th. birthday anniversary</title>
		<link>http://www.mathrix.org/liquid/archives/turings-very-first-universal-machine</link>
		<comments>http://www.mathrix.org/liquid/archives/turings-very-first-universal-machine#comments</comments>
		<pubDate>Tue, 18 May 2010 00:56:45 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Computability, Universality and Unsolvability]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[Minds and Machines]]></category>

		<guid isPermaLink="false">http://www.mathrix.org/liquid/?p=421</guid>
		<description><![CDATA[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. &#8216;Universal&#8217; means that one can &#8216;program&#8217; a general-purpose machine to perform the [...]]]></description>
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		<slash:comments>0</slash:comments>
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		<title>On the Kolmogorov-Chaitin complexity for short sequences</title>
		<link>http://www.mathrix.org/liquid/archives/on-the-kolmogorov-chaitin-complexity-for-short-sequences</link>
		<comments>http://www.mathrix.org/liquid/archives/on-the-kolmogorov-chaitin-complexity-for-short-sequences#comments</comments>
		<pubDate>Wed, 31 Oct 2007 00:44:44 +0000</pubDate>
		<dc:creator>Hector Zenil</dc:creator>
				<category><![CDATA[Algorithmic information theory]]></category>
		<category><![CDATA[Computer Science]]></category>
		<category><![CDATA[Foundations of Computation]]></category>
		<category><![CDATA[New Ideas]]></category>
		<category><![CDATA[algorithmic complexity]]></category>
		<category><![CDATA[Cristian Calude]]></category>
		<category><![CDATA[Jean-Paul Delahaye]]></category>
		<category><![CDATA[John Casti]]></category>
		<category><![CDATA[Paul Davies]]></category>
		<category><![CDATA[randomness]]></category>
		<category><![CDATA[Stephen Wolfram]]></category>

		<guid isPermaLink="false">http://www.mathrix.org/liquid/?p=157</guid>
		<description><![CDATA[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 [...]]]></description>
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