Abstract
The work is concerned with the trade-offs between the dimension and the time and space complexity of computations on nondeterministic cellular automata. It is proved, that
1). Every NCA $\Cal A$ of dimension
r
, computing a predicate
P
with time complexity T(n) and space complexity S(n) can be simulated by
r
-dimensional NCA with time and space complexity
O(
T
1
r+1
S
r
r+1
)
and by
r+1
-dimensional NCA with time and space complexity
O(
T
1/2
+S)
.
2) For any predicate
P
and integer
r>1
if $\Cal A$ is a fastest
r
-dimensional NCA computing
P
with time complexity T(n) and space complexity S(n), then
T=O(S)
.
3). If
T
r,P
is time complexity of a fastest
r
-dimensional NCA computing predicate
P
then $T_{r+1,P} &=O((T_{r,P})^{1-r/(r+1)^2})$, $T_{r-1,P} &=O((T_{r,P})^{1+2/r})$. Similar problems for deterministic CA are discussed.