2 research outputs found
Wolfram's Classification and Computation in Cellular Automata Classes III and IV
We conduct a brief survey on Wolfram's classification, in particular related
to the computing capabilities of Cellular Automata (CA) in Wolfram's classes
III and IV. We formulate and shed light on the question of whether Class III
systems are capable of Turing universality or may turn out to be "too hot" in
practice to be controlled and programmed. We show that systems in Class III are
indeed capable of computation and that there is no reason to believe that they
are unable, in principle, to reach Turing-completness.Comment: 27 pages, 13 figures, forthcoming in Irreducibility and Computational
Equivalence to be published by Springer Verlag
(http://www.mathrix.org/ANKSAnniversaryVolume.html). Extended paper version
to appear in the Journal of Cellular Automata (JCA
Cellular Automata: Reversibility, Semi-reversibility and Randomness
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.Comment: This is my Ph.D thesis defended under the guidance of Dr. Sukanta
Das, Associate Professor, Department of Information Technology, Indian
Institute of Engineering Science and Technology, Shibpur, Howrah, West
Bengal, India - 71110