  In this dissertation, we study two of the global properties of 1-dimensional
cellular automata (CAs) under periodic boundary condition, namely,
reversibility and randomness. To address reversibility of finite CAs, we
develop a mathematical tool, named reachability tree, which can efficiently
characterize those CAs. A decision algorithm is proposed using minimized
reachability tree which takes a CA rule and size n as input and verifies
whether the CA is reversible for that n. To decide reversibility of a finite
CA, we need to know both the rule and the CA size. However, for infinite CAs,
reversibility is decided based on the local rule only. Therefore, apparently,
these two cases seem to be divergent. This dissertation targets to construct a
bridge between these two cases. To do so, reversibility of CAs is redefined and
the notion of semi-reversible CAs is introduced. Hence, we propose a new
classification of finite CAs -(1) reversible CAs, (2) semi-reversible CAs and
(3) strictly irreversible CAs. Finally, relation between reversibility of
finite and infinite CAs is established. This dissertation also explores CAs as
source of randomness and build pseudo-random number generators (PRNGs) based on
CAs. We identify a list of properties for a CA to be a good source of
randomness. Two heuristic algorithms are proposed to synthesize candidate
(decimal) CAs which have great potentiality as PRNGs. Two schemes tare
developed o use these CAs as window-based PRNGs - (1) as decimal number
generators and as (2) binary number generators. We empirically observe that in
comparison to the best PRNG SFMT19937-64, average performance of our proposed
PRNGs are slightly better. Hence, our decimal CAs based PRNGs are one of the
best PRNGs today.
