554 research outputs found
Always Finite Entropy and Lyapunov exponents of two-dimensional cellular automata
Given a new definition for the entropy of a cellular automata acting on a
two-dimensional space, we propose an inequality between the entropy of the
shift on a two-dimensional lattice and some angular analog of Lyapunov
exponents.Comment: 20 Fevrier 200
Density of periodic points, invariant measures and almost equicontinuous points of cellular automata
Revisiting the notion of m-almost equicontinuous cellular automata introduced
by R. Gilman, we show that the sequence of image measures of a shift ergodic
measure m by iterations of a m-almost equicontinuous automata F, converges in
Cesaro mean to an invariant measure mc. If the initial measure m is a
Bernouilli measure, we prove that the Cesaro mean limit measure mc is shift
mixing. Therefore we also show that for any shift ergodic and F-invariant
measure m, the existence of m-almost equicontinuous points implies that the set
of periodic points is dense in the topological support S(m) of the invariant
measure m. Finally we give a non trivial example of a couple (m-equicontinuous
cellular automata F, shift ergodic and F-invariant measure m) which has no
equicontinuous point in S(m)
Some properties of cellular automata with equicontinuity points
We investigate topological and ergodic properties of cellular automata having
equicontinuity points. In this class surjectivity on a transitive SFT implies
existence of a dense set of periodic points. Our main result is that under the
action of such an automaton any shift ergodic measure converges in Cesaro Mean
Entropy rate of higher-dimensional cellular automata
We introduce the entropy rate of multidimensional cellular automata. This
number is invariant under shift-commuting isomorphisms; as opposed to the
entropy of such CA, it is always finite. The invariance property and the
finiteness of the entropy rate result from basic results about the entropy of
partitions of multidimensional cellular automata. We prove several results that
show that entropy rate of 2-dimensional automata preserve similar properties of
the entropy of one dimensional cellular automata.
In particular we establish an inequality which involves the entropy rate, the
radius of the cellular automaton and the entropy of the d-dimensional shift. We
also compute the entropy rate of permutative bi-dimensional cellular automata
and show that the finite value of the entropy rate (like the standard entropy
of for one-dimensional CA) depends on the number of permutative sites.
Finally we define the topological entropy rate and prove that it is an
invariant for topological shift-commuting conjugacy and establish some
relations between topological and measure-theoretic entropy rates
On a zero speed sensitive cellular automaton
Using an unusual, yet natural invariant measure we show that there exists a
sensitive cellular automaton whose perturbations propagate at asymptotically
null speed for almost all configurations. More specifically, we prove that
Lyapunov Exponents measuring pointwise or average linear speeds of the faster
perturbations are equal to zero. We show that this implies the nullity of the
measurable entropy. The measure m we consider gives the m-expansiveness
property to the automaton. It is constructed with respect to a factor dynamical
system based on simple "counter dynamics". As a counterpart, we prove that in
the case of positively expansive automata, the perturbations move at positive
linear speed over all the configurations
A Bilateral version of Shannon-Breiman-McMillan Theorem
We give a new version of the Shannon-McMillan-Breiman theorem in the case of
a bijective action. We illustrate this new result with an exampl
Cellular automata and Lyapunov exponents
In this article we give a new definition of some analog of Lyapunov exponents for cellular automata .Then for a shift ergodic and cellular automaton invariant probability measure we establish an inequality between the entropy of the automaton, the entropy of the shift and the Lyapunov exponent
Developement of simulation tools for the analysis of variability in advanced semiconductor electron devices
The progressive down-scaling has been the driving force behind the integrated circuit (IC) industry for several decades, continuously delivering higher component densities and greater chip functionality, while reducing the cost per function from one CMOS technology generation to the next. Mooreâs law boosts IC industry profits by constantly releasing high-quality and inexpensive electronic applications into the market using new technologies. From the 1 m gate lengths of the eighties to the 35 nm gate lengths of contemporary 22 nm technology, the industry successfully achieved its scaling goals, not only miniaturizing devices but also improving device performance
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