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.