  While binary nearest-neighbour cellar automata (CA) have been studied in
detail and from many different angles, the same cannot be said about ternary
(three-state) CA rules. We present some results of our explorations of a small
subset of the vast space of ternary rules, namely rules possessing additive
invariants. We first enumerate rules with four different additive invariants,
and then we investigate if any of them could be used to construct a two-rule
solution of generalized density classification problem (DCP). We show that
neither simple nor absolute classification is possible with a pair of ternary
rules where the first rule is all-conserving and the second one is reducible to
two states. Similar negative result holds for another version of DCP we
propose: symmetric interval-wise DCP. Finally we show an example of a pair of
rules which solve non-symmetric interval-wise DCP for initial configurations
containing at least one zero.
