[seqfan] 3 more Post-type tag systems

Neil Sloane njasloane at gmail.com
Fri Aug 18 21:51:34 CEST 2017

Post's original tag system from the 1930's
is based on the two strings 00 and 1101.

There are 3 more tag systems of this type that were studied by
Watanabe in 1962. See A284116 for an annotated scan of his paper.

They can be defined by the strings {00,1011}, {00, 1110}, and
{00,0111}.  I just created A291067, -8, -9 for them.

The cross-refs line says:

For the 3-shift tag systems (00,1101}, {00, 1011}, {00, 1110}, {00,
0111} see A284116, A291067, A291068, A291069 respectively (as well as
the cross-referenced entries mentioned there).

All three of the new ones need more terms.  There are also a lot of
other subsidiary sequences that could be added to go with them (just
as A284116 has a lot of cross-referenced children), in case people
would like to help (Don?)

The main open problem is (Allan W. will correct me if I'm wrong) to
decide for the tag systems (00,1101} or {00, 1011} if there is any
starting string that blows up. These are important unsolved questions
going back 80 years or so.  Watanabe appears to assert that for the
systems {00, 1110} and {00, 0111} there are no strings that blow up -
but I did not check his proof.

De Mol (see especially her thesis referenced in A284116) is a bit
critical of the Watanabe paper, and I agree that his Fig 7 doesn't
seem quite right.

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