20190209, 08:24  #1 
"unknown"
Jan 2019
anywhere
13 Posts 
2symbol, 5state Turing machine
Does anyone have the current records for Sigma (2,5) & S (2,5)? I want to obtain full decimal expansion for they...
At the moment we have: Sigma (2,5) > 1.7 * 10^352 S (2,5) > 1.9 * 10^704 
20190209, 21:54  #2 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}·3·883 Posts 
Could you expand on this please? At present I don't know what S (2,5) and Sigma (2,5) mean.
Last fiddled with by xilman on 20190209 at 21:54 
20190209, 22:34  #3 
"Robert Gerbicz"
Oct 2005
Hungary
5×17^{2} Posts 
See https://oeis.org/A028444, this is a quite famous sequence, though it is giving much smaller lower bounds (check the sequences in the comment).
You are attacking very hard problems. 
20190210, 04:04  #4  
"unknown"
Jan 2019
anywhere
13_{10} Posts 
Quote:
Sigma (2,5)  the highest number of nonzero symbols that Turing machine with 2 symbols and 5 states can print. S (2,5)  the same definition, but in this time we have the highest number of steps. 

20190210, 07:25  #5 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10596_{10} Posts 
Thanks both. I'd heard of the busy beaver problem bu not the S & Sigma notation.

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