  In this dissertation, we study temporally stochasticity in cellular automata
and the behavior of such cellular automata. The work also explores the
computational ability of such cellular automaton that illustrates the
computability of solving the affinity classification problem. In addition to
that, a cellular automaton, defined over Cayley tree, is shown as the classical
searching problem solver. The proposed temporally stochastic cellular automata
deals with two elementary cellular automata rules, say $f$ and $g$. The $f$ is
the default rule, however, $g$ is temporally applied to the overall system with
some probability $\tau$ which acts as a noise in the system. After exploring
the dynamics of temporally stochastic cellular automata (TSCAs), we study the
dynamical behavior of these temporally stochastic cellular automata (TSCAs) to
identify the TSCAs that converge to a fixed point from any seed. We apply each
of the convergent TSCAs to some standard datasets and observe the effectiveness
of each TSCA as a pattern classifier. It is observed that the proposed
TSCA-based classifier shows competitive performance in comparison with existing
classifier algorithms. We use temporally stochastic cellular automata to solve
a new problem in the field of cellular automata, named as, affinity
classification problem which is a generalization of the density classification
problem . We show that this model can be used in several applications, like
modeling self-healing systems. Finally, we introduce a new model of computing
unit developed around cellular automata to reduce the workload of the Central
Processing Unit (CPU) of a machine to compute. Each cell of the computing unit
acts as a tiny processing element with attached memory. Such a CA is
implemented on the Cayley Tree to realize efficient solutions for diverse
computational problems.
