Walter Taylor wrote:

>Here is a question that Stephen Bloom asked
>me to place on this list. You may reply to
>him at bloom@....
>
>Are there charaterization theorems for models
>of balanced, regular equations? (Sometimes
>these are called super regular equations.)
>
>An equation s=t is balanced, and regular if
>var(s)=var(t) and no variable
>appears more than once in each list, where
>
>v(s)=s, if s is a variable and
>
>v( f(t1,...tk) ) is the concatenation
> v(t1) v(t2) ... v(tk), where f is a function symbol of rank k.
>
>So, for example,
> x.(y.z) = (x.y).z
>is regular and balanced, but
> x.y = y.x
>is not. The ordering of the variables counts.
>
There is something missing in the definition (links please). What is v ?
Apparently v is an interpretation on a groupoid of the original terms.

A. Mani
Member, Cal. Math. Soc.