  The purpose of the present study is to search one-dimensional Cellular
Automata (CA) rules which will solve the density classification task (DCT)
perfectly. The mathematical analysis of number conserving functions over binary
strings of length n gives an indication of its corresponding number conserving
cellular automata rules (either uniform or non-uniform). The state transition
diagrams (STDs) of number conserving CA rules have been analyzed where it has
been found that these STDs can generate different DCT solutions. While studying
the properties of STDs, an interesting classification of binary strings could
be made where equal weight strings form a class and the cardinality of each
class is same as the binomial coefficient nCk; n is the length and k is the
weight of the binary string. Apart from STDs, other deterministic methods have
been proposed to obtain the exact solution of DCT. All these exact solutions of
DCT using different deterministic methods can be viewed as an improvement over
the soft computing techniques used earlier to obtain approximate solutions.
