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A337537
Period of orbit of Post's tag system ({0,1},{(0,0101100),(1,11000111100000)},10,(1+0^9)^n).
1
7, 7, 7, 7, 7, 308, 7, 308, 308, 112, 308, 308, 140, 308, 140, 3429251, 140, 308, 140, 802613, 3429251, 140, 140, 3429251, 802613, 3429251, 3429251, 3429251, 3429251, 3429251, 140, 140, 802613, 3429251, 802613, 802613, 140, 802613, 140, 802613, 802613, 3429251
OFFSET
1,1
COMMENTS
In general a tag as defined by Emil Leon Post, is given by a 4-tuple (Sigma,AF,n,w0), where Sigma is some (nonempty) set of symbols called the alphabet, AF is the associated function (sometimes also called set of production rules) AF: Sigma -> Sigma*, n is the deletion number and w0 the initial string.
From the starting sequence we obtain a new string in each step by adjoining the string associated to the prefix symbol of the string, where after the prefix n symbols are removed from the string.
The decision problem is: will the tag end up in an empty string, a(n) = 0 or not, a(n) <> 0?
This tag system was proposed by Liesbeth De Mol (p. 329).
a(n) == 0 (mod 7). Proof: for each cycle four times the number of associations (productions) 0 -> 0101100 must equal three times the number of associations (productions) 1 -> 11000111100000 applied within a cycle.
LINKS
Emil L. Post, Formal reductions of the general combinatorial decision problem., American Journal of Mathematics, Vol. 65, No. 2 (Apr., 1943), pp. 197-215.
Eric Weisstein's World of Mathematics, Tag System
CROSSREFS
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Aug 31 2020
STATUS
approved