Instantaneous Description

Definition 4: The instantaneous description id of an an active index IX is denoted by id = (<ic>, <s>, <oL>), where <ic> is the ic vector, <s> is the corresponding state vector, and <oL> is the corresponding output list vector.

Definition 5: The trace of an active index IX with respect to (<ic0>, <s0>, <oL0>) is: 

(<ic0>, <s0>, <oL0>) =>  
(<ic1>, <s1>, <oL1>) =>
.....
(<icn>, <sn>, <oLn>)
where (<ici>, <si>, <oLi>) => (<ici+1>, <si+1>, <oLi+1>) due to the acceptance of input messages by an index cell. The => symbol reads as "is transformed into". Such transformations may occur in any arbitrary order. Each transformation step in the trace takes exactly one clock cycle. If the trace is finite, the active index IX is terminating with respect to (<ic0>, <s0>, <oL0>); otherwise it is nonterminating.