From this paper.
"A (bi-directional, deterministic) cellular automaton is a triplet $A = (S;N;\delta)$, where $S$ is an non-empty state set, $N$ is the neighborhood system, and $\delta$ is the local transition function (rule). This function defines the rule of calculating the cell’s state at $t +1$ time step, given the states of the neighborhood cells at previous time step $t$"
I haven't found other "bidirectional" CA via Google, so I wonder what does the term say about this automaton's properties. Does it mean that the state $t+1$ can be used to find out the state $t$?
