7,404 research outputs found
Bulking II: Classifications of Cellular Automata
This paper is the second part of a series of two papers dealing with bulking:
a way to define quasi-order on cellular automata by comparing space-time
diagrams up to rescaling. In the present paper, we introduce three notions of
simulation between cellular automata and study the quasi-order structures
induced by these simulation relations on the whole set of cellular automata.
Various aspects of these quasi-orders are considered (induced equivalence
relations, maximum elements, induced orders, etc) providing several formal
tools allowing to classify cellular automata
Intrinsically universal one-dimensional quantum cellular automata in two flavours
We give a one-dimensional quantum cellular automaton (QCA) capable of
simulating all others. By this we mean that the initial configuration and the
local transition rule of any one-dimensional QCA can be encoded within the
initial configuration of the universal QCA. Several steps of the universal QCA
will then correspond to one step of the simulated QCA. The simulation preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. The encoding is linear and hence
does not carry any of the cost of the computation. We do this in two flavours:
a weak one which requires an infinite but periodic initial configuration and a
strong one which needs only a finite initial configuration. KEYWORDS: Quantum
cellular automata, Intrinsic universality, Quantum computation.Comment: 27 pages, revtex, 23 figures. V3: The results of V1-V2 are better
explained and formalized, and a novel result about intrinsic universality
with only finite initial configurations is give
Upper Bound on the Products of Particle Interactions in Cellular Automata
Particle-like objects are observed to propagate and interact in many
spatially extended dynamical systems. For one of the simplest classes of such
systems, one-dimensional cellular automata, we establish a rigorous upper bound
on the number of distinct products that these interactions can generate. The
upper bound is controlled by the structural complexity of the interacting
particles---a quantity which is defined here and which measures the amount of
spatio-temporal information that a particle stores. Along the way we establish
a number of properties of domains and particles that follow from the
computational mechanics analysis of cellular automata; thereby elucidating why
that approach is of general utility. The upper bound is tested against several
relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables,
http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and
accompanying text modified, to comply with legal demands arising from
on-going intellectual property litigation among third parties. V3: Accepted
for publication in Physica D. References added and other small changes made
per referee suggestion
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
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