\subset P$. $S$ is called the ‘separable class’ if the following conditions hold.

-   $S \subset S_2$

-   If $f$ is a prenex formula and $F$ is it’s decomposition, $\forall f \in F$, $\exists x_i \in \{x_1,...,x_n\}$ such that $f$ is independent of $x_i$.

The property of separability is not uniform in this separable class. It depends heavily on the sharing factor of the formula. The quantification of the term structure enables us to define the ‘centre of $S_k$’ for $k < K$.

The centre of $S_k$ is the set of all prenex formulae, $f$ in $n$ variables ($x_1, . . . ,x_n$) with decomposition $F$, such that the clause $f_i \in F$ contains exactly the variables $x_{\frac{i-1}{k}+1}, . . . ,x_{\frac{i}{k}}$.

Unlike the classes $S_1, . . . ,S_k$, the classes $C_1, . . . ,C_k$ do not form a nesting chain structure. In other words, $C_i$ need not contain $C_{i+1}$.

This centre of a separable class, $S_i$, is the set of formulae which pose a ‘best case’ scenario for the CAD algorithm to run in parallel for an input prenex formula containing $i$ variables. The lower the maximum sharing factor in a prenex formula, the faster it’s execution 