Definition 2: The output list oL of an ic is of the following form: [(Ic₁, y₁), (Ic₂, y₂), ..., (Ic_m, y_m)], where y_i is the output message posted to the ic's in the set Ic_i. If any ic in Ic_i accepts y_i, the tuple (Ic_i, y_i) is removed from the output list.

Definition 3: An index cell base ICB is a (possibly infinite) collection of index cells. Given an index cell base ICB, an active index IX is a finite subset of ICB with n index cells, denoted by an n-place ic vector <ic> = (ic₁, ic₂, ..., ic_n), where the ic's are ordered by their (arbitrary) subscripts in ICB.