1,177 research outputs found
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Cellular Automata as a Model of Physical Systems
Cellular Automata (CA), as they are presented in the literature, are abstract
mathematical models of computation. In this pa- per we present an alternate
approach: using the CA as a model or theory of physical systems and devices.
While this approach abstracts away all details of the underlying physical
system, it remains faithful to the fact that there is an underlying physical
reality which it describes. This imposes certain restrictions on the types of
computations a CA can physically carry out, and the resources it needs to do
so. In this paper we explore these and other consequences of our
reformalization.Comment: To appear in the Proceedings of AUTOMATA 200
Phase Space Invertible Asynchronous Cellular Automata
While for synchronous deterministic cellular automata there is an accepted
definition of reversibility, the situation is less clear for asynchronous
cellular automata. We first discuss a few possibilities and then investigate
what we call phase space invertible asynchronous cellular automata in more
detail. We will show that for each Turing machine there is such a cellular
automaton simulating it, and that it is decidable whether an asynchronous
cellular automaton has this property or not, even in higher dimensions.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Post-surjectivity and balancedness of cellular automata over groups
We discuss cellular automata over arbitrary finitely generated groups. We
call a cellular automaton post-surjective if for any pair of asymptotic
configurations, every pre-image of one is asymptotic to a pre-image of the
other. The well known dual concept is pre-injectivity: a cellular automaton is
pre-injective if distinct asymptotic configurations have distinct images. We
prove that pre-injective, post-surjective cellular automata are reversible.
Moreover, on sofic groups, post-surjectivity alone implies reversibility. We
also prove that reversible cellular automata over arbitrary groups are
balanced, that is, they preserve the uniform measure on the configuration
space.Comment: 16 pages, 3 figures, LaTeX "dmtcs-episciences" document class. Final
version for Discrete Mathematics and Theoretical Computer Science. Prepared
according to the editor's request
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