A family of grammars for Voynichese

[Jorge_Stolfi]

I’m curious what happens if you don’t include gallows as part of K (except the bench ones because they still have the underlying ch).

Good point.  Lumping the platform gallows (CTh etc) with simple gallows (t etc) is a potential defect of the "crust-mantle-core" (CMC) model as I formulated it, because former should contribute to the count of benches "X".  Maybe as half a bench in the prefix, half in the suffix.  

While we think about that issue, here are some counts that don't depend on it.  I we delete the "O"s and map each element to its class "Q", "D", "X" etc, we get the "CMC pattern" of the word.  If the word has no gallows ("H") and no benches ("X"), a valid CMC pattern must be Q^q D^d+e N^n where q and n are 0 or 1, and d+e is between 0 and 3.  Recall that 

• "Q" is just {q}, 
  
• "D" (the "dealers") are {d} {l} {r} {s}
  
• "N" is {n}, {m}, {in}, {im}, {ir}, ...{iir}, {iiin}, {iiim}
  

Here are the counts:

COUNTING CRUST-ONLY TOKENS BY CMC PATTERN

   2433.187500 0.30517 D
   2034.375000 0.25515 DN
   1552.062500 0.19466 DD
    849.250000 0.10651 N
    286.500000 0.03593 -
    225.750000 0.02831 QD
    217.375000 0.02726 DDD
    148.562500 0.01863 DDN
     83.500000 0.01047 QDN
     47.000000 0.00589 Q
     44.250000 0.00555 QN
     34.000000 0.00426 QDD
     15.437500 0.00194 DDDN
      2.000000 0.00025 QDDD

There are 2 x 4 x 2 = 16 CMC patterns that fit the formula above.  Here they are sorted "alphabetically" instead of by frequency:

    217.375000 0.02726 DDD
   1552.062500 0.19466 DD
   2433.187500 0.30517 D
    286.500000 0.03593 -
   
     15.437500 0.00194 DDDN
    148.562500 0.01863 DDN
   2034.375000 0.25515 DN
    849.250000 0.10651 N
   
      2.000000 0.00025 QDDD
     34.000000 0.00426 QDD
    225.750000 0.02831 QD
     47.000000 0.00589 Q
     
      0.0      0.0     QDDDN
      0.0      0.0     QDDN
     83.500000 0.01047 QDN
     44.250000 0.00555 QN

The patterns "QDDDN" and "QDDN" are absent, and "QDDD" is down at noise level.   Maybe the limit should be q+d+e+n <= 3, rather than just d+e <= 3.  But let me first see what happens when there are "X" and "H"...

All the best, --stolfi