  A cellular automaton that is a generalization of the box-ball system with
either many kinds of balls or finite carrier capacity is proposed and studied
through two discrete integrable systems: nonautonomous discrete KP lattice and
nonautonomous discrete two-dimensional Toda lattice. Applying reduction
technique and ultradiscretization procedure to these discrete systems, we
derive two types of time evolution equations of the proposed cellular
automaton, and particular solutions to the ultradiscrete equations.
