Busy beaver machines and the observant otter heuristic

The busy beaver problem is to find the maximum number of non-zero characters that can be printed by an n-state Turing machine of a particular type. A critical step in the solution of this problem is to determine whether or not a given n-state Turing machine halts on a blank input. Given the enormous output sizes that can be produced by some small machines, it becomes critical to have appropriate methods for dealing with the exponential behaviour of both terminating and nonterminating machines. In this paper, we investigate a heuristic which can be used to greatly accelerateexecution of this class of machines. This heuristic, which we call the observant otter, is based on the detection of patterns earlier in the execution trace. We describe our implementation of this method and report various experimental results based on it, including showing how it can be used to evaluate all known 'monster' machines, including some whose naive execution would take around 10^36,534 steps

How incomputable is Kolmogorov complexity?

Kolmogorov complexity is the length of the ultimately compressed version of a file (that is, anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the incomputabilty of Kolmogorov complexity, which formal loopholes this leaves us, recent approaches to compute or approximate Kolmogorov complexity, which approaches are problematic and which approaches are viable.Comment: 9 pages LaTe

The Busy Beaver Competition: a historical survey

Tibor Rado defined the Busy Beaver Competition in 1962. He used Turing machines to give explicit definitions for some functions that are not computable and grow faster than any computable function. He put forward the problem of computing the values of these functions on numbers 1, 2, 3, ... More and more powerful computers have made possible the computation of lower bounds for these values. In 1988, Brady extended the definitions to functions on two variables. We give a historical survey of these works. The successive record holders in the Busy Beaver Competition are displayed, with their discoverers, the date they were found, and, for some of them, an analysis of their behavior.Comment: 70 page

The Busy Beaver Competition: a historical survey

70 pagesTibor Rado defined the Busy Beaver Competition in 1962. He used Turing machines to give explicit definitions for some functions that are not computable and grow faster than any computable function. He put forward the problem of computing the values of these functions on numbers 1, 2, 3, ... More and more powerful computers have made possible the computation of lower bounds for these values. In 1988, Brady extended the definitions to functions on two variables. We give a historical survey of these works. The successive record holders in the Busy Beaver Competition are displayed, with their discoverers, the date they were found, and, for some of them, an analysis of their behavior

A Holmes and Doyle Bibliography, Volume 9: All Formats—Combined Alphabetical Listing

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. This volume contains all listings in all formats, arranged alphabetically by author or main entry. In other words, it combines the listings from Volume 1 (Monograph and Serial Titles), Volume 3 (Periodical Articles), and Volume 7 (Audio/Visual Materials) into a comprehensive bibliography. (There may be additional materials included in this list, e.g. duplicate items and items not yet fully edited.) As in the other volumes, coverage of this material begins around 1994, the final year covered by De Waal's bibliography, but may not yet be totally up-to-date (given the ongoing nature of this bibliography). It is hoped that other titles will be added at a later date. At present, this bibliography includes 12,594 items

A Holmes and Doyle Bibliography, Volume 5: Periodical Articles--Secondary References, Alphabetical Listing

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. Volume 5 includes "passing" or "secondary" references, i.e. those entries that are passing in nature or contain very brief information or content

A Holmes and Doyle Bibliography, Volume 6: Periodical Articles, Subject Listing, By De Waal Category

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. Volume 6 presents the periodical literature arranged by subject categories (as originally devised for the De Waal bibliography and slightly modified here)