X is the (possibly infinite) set of input messages including dummy input *d*.

Y is the (possibly infinite) set of output messages including dummy output *d*.

S is the (possibly infinite) set of states. S includes a
set of ordinary states **S** and a special state s_{dead} called the dead state. If an index cell is in the dead state, it is a dead index cell. Otherwise it
is a live index cell.

s_{o} in **S** is the initial state of the index cell ic.

A is the set of action sequences that can be performed by this index cell.

t_{max} is the maximum time for the cell to remain live, without receiving any messages. If t_{max} is infinite, the cell is perennial.