  In this paper, we study the lattice linearity of multiplication and modulo
operations. We demonstrate that these operations are lattice linear and the
parallel processing algorithms that we study for both these operations are able
to exploit the lattice linearity of their respective problems. This implies
that these algorithms can be implemented in asynchronous environments, where
the nodes are allowed to read old information from each other. These algorithms
also exhibit snap-stabilizing properties, i.e., starting from an arbitrary
state, the sequence of state transitions made by the system strictly follows
its specification.
