B. Hasslacher, D.A. Meyer, Knot Invariants and Cellular Automata, Physica D
   45 (1990) 328-344.

If we take the general A,B,d bracket on the left and right hand sides of
each of the Reidemeister moves, we get R2 and R3 giving us the unnormalized
Jones Polynomials.  To get R1, we have to normalize.

Tensor notation:

 ab                                              
S   means a -> d overlaid by b -> c (writhe = +1)
 cd                                              

_ab                                             
S   means a -> d overlaying b -> c (writhe = -1)
 cd                                             

     a      b                                         
delta  delta  means a -> c and b -> d without crossing
     c      d                                         

Then the oriented Reidemeister moves R2a, R2b, and the noncyclic R3a correspond
to:

            ab _ij        a      b
unitarity: S   S   = delta  delta 
            ij  cd        c      d

                          ec _bd        e      b
cross-channel unitarity: S   S   = delta  delta 
                          fd  ac        a      f

              ab  tg  rl    bg  ar  lt
Yang-Baxter: S   S   S   = S   S   S  
              rt  ls  mu    rt  ml  us

The quantum Yang-Baxter condition is given by:

 ab     jc         ik       bc     ai         kj   
S  (u) S  (u + v) S  (v) = S  (v) S  (u + v) S  (u)
 ij     kf         de       ij     dk         ef   

where u is the rapidity (spectral parameter).

To get from this to the R3a, we must suppress the rapidity dependence.
It turns out this can be done only if the models are critical.

So we take the additive invariants F(a,b,c,d) and use

 ab    -F(a,b,c,d)/k T    F(a,b,c,d)
S   = e                = x          
 cd                                 

and test if the oriented Reidemeister moves hold.  If so, then the system
is solvable.  Apparently, a,b,c,d are either 0 or 1.

What we have done is to use the additive invariants to determine solvability.
Examples the authors give for F that lead to solvable models are

                    2          2
F(a,b,c,d) = (a - d)  + (b - c) 

                    2          2
F(a,b,c,d) = (b - c)  - (a - d)