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Latest Busy Beaver champion has too many digits to count

86 点作者 nickdrozd将近 3 年前

5 条评论

fn-mote将近 3 年前
This looks like a really cool topic... but you need to know the basic definitions in order to understand the article or its parent.<p><a href="https:&#x2F;&#x2F;webusers.imj-prg.fr&#x2F;~pascal.michel&#x2F;tmi.html" rel="nofollow">https:&#x2F;&#x2F;webusers.imj-prg.fr&#x2F;~pascal.michel&#x2F;tmi.html</a><p>Quoted so you don&#x27;t have to dig for it:<p><pre><code> What is a busy beaver? Consider Turing machines with fixed numbers of states and symbols. If there are k states and n symbols, then the number of possible next move functions, or possible tables, is (2kn+1)^kn. Thus, there are (2kn+1)^kn Turing machines with k states and n symbols. Each of them can be launched on a blank tape, that is a tape with symbols 0 in all cells. Then some of them never stop, and the other ones eventually stop. Those which stop are called busy beavers. Busy beavers compete in two competitions: to take the most time to stop, to leave the most non-blank symbols on the tape when stopping.</code></pre>
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sligocki将近 3 年前
Hello, I&#x27;m the author. Ask me anything :)<p>Thanks fn-mote for providing some context. In fact, I think you could appreciate most of this article without even knowing anything about Turing Machines. I spend almost the entire article just answering the question: Given a set of exponential transition rules, starting from C(5), does iterating these rules ever lead to Halt(N)? If so, in how many iterations? And what is the value of N in that case?
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flobosg将近 3 年前
Related: “Who Can Name the Bigger Number?” – <a href="https:&#x2F;&#x2F;www.scottaaronson.com&#x2F;writings&#x2F;bignumbers.html" rel="nofollow">https:&#x2F;&#x2F;www.scottaaronson.com&#x2F;writings&#x2F;bignumbers.html</a>
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AlbertoGP将近 3 年前
Ah, fond memories of first learning about Busy Beavers in A.K.Dewdney’s column in the Spanish edition of Scientific American (“Investigación y Ciencia”) as a kid: <a href="https:&#x2F;&#x2F;www.investigacionyciencia.es&#x2F;revistas&#x2F;investigacion-y-ciencia&#x2F;monumento-azteca-161&#x2F;una-trampa-computarizada-del-castor-afanoso-la-ms-productiva-de-las-mquinas-de-turing-2062" rel="nofollow">https:&#x2F;&#x2F;www.investigacionyciencia.es&#x2F;revistas&#x2F;investigacion-...</a><p>I made my own Turing Machine emulator for my Commodore 64 to play with this, using the screen memory as tape to speed it up: modifying the tape was immediately reflected on the screen with no other processing needed, saving precious cycles.<p>That made for quite a small tape, but allowed even my crude BASIC implementation to run fast, or so I remember it.<p>The original article in English appeared in the August 1984 magazine, and the translated ones in October of that same year: <a href="https:&#x2F;&#x2F;www.jstor.org&#x2F;stable&#x2F;24969427" rel="nofollow">https:&#x2F;&#x2F;www.jstor.org&#x2F;stable&#x2F;24969427</a><p>If you can read Russian or Italian, you can find the full article here:<p>Russian: <a href="https:&#x2F;&#x2F;gudleifr.forum2x2.ru&#x2F;t98-topic#1254" rel="nofollow">https:&#x2F;&#x2F;gudleifr.forum2x2.ru&#x2F;t98-topic#1254</a><p>Italian: <a href="https:&#x2F;&#x2F;archive.org&#x2F;details&#x2F;divertirsiconilcalcolatore&#x2F;page&#x2F;n85&#x2F;mode&#x2F;2up" rel="nofollow">https:&#x2F;&#x2F;archive.org&#x2F;details&#x2F;divertirsiconilcalcolatore&#x2F;page&#x2F;...</a><p>I quote the historical introduction from the English version:<p>&gt; “<i>With the possible exception of bees, beavers are the busiest animals alive. All day they ply quiet northern waters bringing twigs and branches to their dam. It was undoubtedly this behavior that led Tibor Rado of Ohio State University to name a certain Turing-machine problem the Busy Beaver Game. In the early 1960’s Rado wondered how many 1’s a Turing machine could be made to print before it halted. Specifically, if a Turing machine with n possible states begins to work on a tape filled with 0’s, what is the largest number of 1’s it can print on the tape before coming to a stop? The answer is known for n = 1, n = 2, n = 3, and n = 4 but not for n = 5 or for any value of n grater than 5.</i>”
tim_hutton将近 3 年前
As a Golly file, so you can run it for yourself: <a href="https:&#x2F;&#x2F;github.com&#x2F;GollyGang&#x2F;ruletablerepository&#x2F;raw&#x2F;gh-pages&#x2F;downloads&#x2F;PavelKropitz_t15.zip" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;GollyGang&#x2F;ruletablerepository&#x2F;raw&#x2F;gh-page...</a> (4kB)<p>In Golly: File &gt; Open Pattern... &gt; open the zip itself (don&#x27;t unzip first).