2,128 research outputs found
Finding The Sign Of A Function Value By Binary Cellular Automaton
Given a continuous function , suppose that the sign of only has
finitely many discontinuous points in the interval . We show how to use
a sequence of one dimensional deterministic binary cellular automata to
determine the sign of where is the (number) density of 1s in
an arbitrarily given bit string of finite length provided that satisfies
certain technical conditions.Comment: Revtex, uses amsfonts, 10 page
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
Extracting Boolean rules from CA patterns
A multiobjective genetic algorithm (GA) is introduced to identify both the neighborhood and the rule set in the form of a parsimonious Boolean expression for both one- and two-dimensional cellular automata (CA). Simulation results illustrate that the new algorithm performs well even when the patterns are corrupted by static and dynamic nois
Hierarchical Economic Agents and their Interactions
We present a new type of spin market model, populated by hierarchical agents,
represented as configurations of sites and arcs in an evolving network. We
describe two analytic techniques for investigating the asymptotic behavior of
this model: one based on the spectral theory of Markov chains and another
exploiting contingent submartingales to construct a deterministic cellular
automaton that approximates the stochastic dynamics. Our study of this system
documents a phase transition between a sub-critical and a super-critical regime
based on the values of a coupling constant that modulates the tradeoff between
local majority and global minority forces. In conclusion, we offer a
speculative socioeconomic interpretation of the resulting distributional
properties of the system.Comment: 38 pages, 13 figures, presented at the 2013 WEHIA conference; to
appear in Journal of Economic Interaction and Coordination, to appear in
Journal of Economic Interaction and Coordinatio
Density classification on infinite lattices and trees
Consider an infinite graph with nodes initially labeled by independent
Bernoulli random variables of parameter p. We address the density
classification problem, that is, we want to design a (probabilistic or
deterministic) cellular automaton or a finite-range interacting particle system
that evolves on this graph and decides whether p is smaller or larger than 1/2.
Precisely, the trajectories should converge to the uniform configuration with
only 0's if p1/2. We present solutions to that problem
on the d-dimensional lattice, for any d>1, and on the regular infinite trees.
For Z, we propose some candidates that we back up with numerical simulations
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