8,031 research outputs found
Directed Percolation arising in Stochastic Cellular Automata
12 pagesCellular automata are both seen as a model of computation and as tools to model real life systems. Historically they were studied under synchronous dynamics where all the cells of the system are updated at each time step. Meanwhile the question of probabilistic dynamics emerges: on the one hand, to develop cellular automata which are capable of reliable computation even when some random errors occur; on the other hand, because synchronous dynamics is not a reasonable assumption to simulate real life systems. Among cellular automata a specific class was largely studied in synchronous dynamics : the elementary cellular automata (ECA). These are the "simplest" cellular automata. Nevertheless they exhibit complex behaviors and even Turing universality. Several studies have focused on this class under alpha-asynchronous dynamics where each cell has a probability alpha to be updated independently. It has been shown that some of these cellular automata exhibit interesting behavior such as phase transition when the asynchronicity rate alpha varies. Due to their richness of behavior, probabilistic cellular automata are also very hard to study. Almost nothing is known of their behavior. Understanding these "simple" rules is a key step to analyze more complex systems. We present here a coupling between oriented percolation and ECA 178 and confirms previous observations that percolation may arise in cellular automata. As a consequence this coupling shows that there is a positive probability that the ECA 178 does not reach a stable configuration with positive probability as soon as the initial configuration is not a stable configuration and alpha > 0.996. Experimentally, this result seems to stay true as soon as alpha > alpha_c where alpha_c is almost 0.5
Failover in cellular automata
A cellular automata (CA) configuration is constructed that exhibits emergent
failover. The configuration is based on standard Game of Life rules. Gliders
and glider-guns form the core messaging structure in the configuration. The
blinker is represented as the basic computational unit, and it is shown how it
can be recreated in case of a failure. Stateless failover using primary-backup
mechanism is demonstrated. The details of the CA components used in the
configuration and its working are described, and a simulation of the complete
configuration is also presented.Comment: 16 pages, 15 figures and associated video at
http://dl.dropbox.com/u/7553694/failover_demo.avi and simulation at
http://dl.dropbox.com/u/7553694/failover_simulation.ja
-Limit Sets of Cellular Automata from a Computational Complexity Perspective
This paper concerns -limit sets of cellular automata: sets of
configurations made of words whose probability to appear does not vanish with
time, starting from an initial -random configuration. More precisely, we
investigate the computational complexity of these sets and of related decision
problems. Main results: first, -limit sets can have a -hard
language, second, they can contain only -complex configurations, third,
any non-trivial property concerning them is at least -hard. We prove
complexity upper bounds, study restrictions of these questions to particular
classes of CA, and different types of (non-)convergence of the measure of a
word during the evolution.Comment: 41 page
Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise
Thermal noise in a cellular automaton refers to a random perturbation to its
function which eventually leads this automaton to an equilibrium state
controlled by a temperature parameter. We study the 1-dimensional majority-3
cellular automaton under this model of noise. Without noise, each cell in this
automaton decides its next state by majority voting among itself and its left
and right neighbour cells. Transfer matrix analysis shows that the automaton
always reaches a state in which every cell is in one of its two states with
probability 1/2 and thus cannot remember even one bit of information. Numerical
experiments, however, support the possibility of reliable computation for a
long but finite time.Comment: 12 pages, 4 figure
Fault Tolerance in Cellular Automata at High Fault Rates
A commonly used model for fault-tolerant computation is that of cellular
automata. The essential difficulty of fault-tolerant computation is present in
the special case of simply remembering a bit in the presence of faults, and
that is the case we treat in this paper. We are concerned with the degree (the
number of neighboring cells on which the state transition function depends)
needed to achieve fault tolerance when the fault rate is high (nearly 1/2). We
consider both the traditional transient fault model (where faults occur
independently in time and space) and a recently introduced combined fault model
which also includes manufacturing faults (which occur independently in space,
but which affect cells for all time). We also consider both a purely
probabilistic fault model (in which the states of cells are perturbed at
exactly the fault rate) and an adversarial model (in which the occurrence of a
fault gives control of the state to an omniscient adversary). We show that
there are cellular automata that can tolerate a fault rate (with
) with degree , even with adversarial combined
faults. The simplest such automata are based on infinite regular trees, but our
results also apply to other structures (such as hyperbolic tessellations) that
contain infinite regular trees. We also obtain a lower bound of
, even with purely probabilistic transient faults only
Cellular automaton supercolliders
Gliders in one-dimensional cellular automata are compact groups of
non-quiescent and non-ether patterns (ether represents a periodic background)
translating along automaton lattice. They are cellular-automaton analogous of
localizations or quasi-local collective excitations travelling in a spatially
extended non-linear medium. They can be considered as binary strings or symbols
travelling along a one-dimensional ring, interacting with each other and
changing their states, or symbolic values, as a result of interactions. We
analyse what types of interaction occur between gliders travelling on a
cellular automaton `cyclotron' and build a catalog of the most common
reactions. We demonstrate that collisions between gliders emulate the basic
types of interaction that occur between localizations in non-linear media:
fusion, elastic collision, and soliton-like collision. Computational outcomes
of a swarm of gliders circling on a one-dimensional torus are analysed via
implementation of cyclic tag systems
A Computation in a Cellular Automaton Collider Rule 110
A cellular automaton collider is a finite state machine build of rings of
one-dimensional cellular automata. We show how a computation can be performed
on the collider by exploiting interactions between gliders (particles,
localisations). The constructions proposed are based on universality of
elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and
computing on rings.Comment: 39 pages, 32 figures, 3 table
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