1,113 research outputs found
A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings
In this paper we investigate certain properties of semi-totalistic cellular
automata (CA) on the well known quasi-periodic kite and dart two dimensional
tiling of the plane presented by Roger Penrose. We show that, despite the
irregularity of the underlying grid, it is possible to devise a semi-totalistic
CA capable of simulating any boolean circuit on this aperiodic tiling.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Computational universes
Suspicions that the world might be some sort of a machine or algorithm
existing ``in the mind'' of some symbolic number cruncher have lingered from
antiquity. Although popular at times, the most radical forms of this idea never
reached mainstream. Modern developments in physics and computer science have
lent support to the thesis, but empirical evidence is needed before it can
begin to replace our contemporary world view.Comment: Several corrections of typos and smaller revisions, final versio
Computation and construction universality of reversible cellular automata
An arbitrary d-dimensional cellular automaton can be constructively embedded in areversible one having d+1 dimensions. In particular, there exist computation- and construction-universal reversible cellular automata. Thus, we explicitly show a way of implementing nontrivial irreversible processes in a reversible medium. Finally, we derive new results for the bounding problem for configurations, both in general and for reversible cellular automata
Computational Processes and Incompleteness
We introduce a formal definition of Wolfram's notion of computational process
based on cellular automata, a physics-like model of computation. There is a
natural classification of these processes into decidable, intermediate and
complete. It is shown that in the context of standard finite injury priority
arguments one cannot establish the existence of an intermediate computational
process
When--and how--can a cellular automaton be rewritten as a lattice gas?
Both cellular automata (CA) and lattice-gas automata (LG) provide finite
algorithmic presentations for certain classes of infinite dynamical systems
studied by symbolic dynamics; it is customary to use the term `cellular
automaton' or `lattice gas' for the dynamic system itself as well as for its
presentation. The two kinds of presentation share many traits but also display
profound differences on issues ranging from decidability to modeling
convenience and physical implementability.
Following a conjecture by Toffoli and Margolus, it had been proved by Kari
(and by Durand--Lose for more than two dimensions) that any invertible CA can
be rewritten as an LG (with a possibly much more complex ``unit cell''). But
until now it was not known whether this is possible in general for
noninvertible CA--which comprise ``almost all'' CA and represent the bulk of
examples in theory and applications. Even circumstantial evidence--whether in
favor or against--was lacking.
Here, for noninvertible CA, (a) we prove that an LG presentation is out of
the question for the vanishingly small class of surjective ones. We then turn
our attention to all the rest--noninvertible and nonsurjective--which comprise
all the typical ones, including Conway's `Game of Life'. For these (b) we prove
by explicit construction that all the one-dimensional ones are representable as
LG, and (c) we present and motivate the conjecture that this result extends to
any number of dimensions.
The tradeoff between dissipation rate and structural complexity implied by
the above results have compelling implications for the thermodynamics of
computation at a microscopic scale.Comment: 16 page
MFCS\u2798 Satellite Workshop on Cellular Automata
For the 1998 conference on Mathematical Foundations of Computer
Science (MFCS\u2798) four papers on Cellular Automata were accepted as
regular MFCS\u2798 contributions. Furthermore an MFCS\u2798 satellite
workshop on Cellular Automata was organized with ten additional talks.
The embedding of the workshop into the conference with its
participants coming from a broad spectrum of fields of work lead to
interesting discussions and a fruitful exchange of ideas.
The contributions which had been accepted for MFCS\u2798 itself may be
found in the conference proceedings, edited by L. Brim, J. Gruska and
J. Zlatuska, Springer LNCS 1450. All other (invited and regular)
papers of the workshop are contained in this technical report. (One
paper, for which no postscript file of the full paper is available, is
only included in the printed version of the report).
Contents:
F. Blanchard, E. Formenti, P. Kurka: Cellular automata in the Cantor,
Besicovitch and Weyl Spaces
K. Kobayashi: On Time Optimal Solutions of the Two-Dimensional Firing
Squad Synchronization Problem
L. Margara: Topological Mixing and Denseness of Periodic Orbits for
Linear Cellular Automata over Z_m
B. Martin: A Geometrical Hierarchy of Graph via Cellular Automata
K. Morita, K. Imai: Number-Conserving Reversible Cellular Automata and
Their Computation-Universality
C. Nichitiu, E. Remila: Simulations of graph automata
K. Svozil: Is the world a machine?
H. Umeo: Cellular Algorithms with 1-bit Inter-Cell Communications
F. Reischle, Th. Worsch: Simulations between alternating CA,
alternating TM and circuit families
K. Sutner: Computation Theory of Cellular Automat
Translating partitioned cellular automata into classical type cellular automata
ISBN 978-5-94057-377-7International audiencePartitioned cellular automata are a variant of cellular automata that was defined in order to make it very simple to create complex automata having strong properties such as number conservation and reversibility (which are often difficult to obtain on cellular automata). In this article we show how a partitioned cellular automaton can be translated into a regular cellular automaton in such a way that these properties are conserved
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