4 research outputs found
Stable Multi-Level Monotonic Eroders
Eroders are monotonic cellular automata with a linearly ordered state set
that eventually wipe out any finite island of nonzero states. One-dimensional
eroders were studied by Gal'perin in the 1970s, who presented a simple
combinatorial characterization of the class. The multi-dimensional case has
been studied by Toom and others, but no such characterization has been found.
We prove a similar characterization for those one-dimensional monotonic
cellular automata that are eroders even in the presence of random noise.Comment: 32 pages, 9 figure
Stable Multi-Level Monotonic Eroders
Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal'perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise
Simply modified GKL density classifiers that reach consensus faster
The two-state Gacs-Kurdyumov-Levin (GKL) cellular automaton has been a staple
model in the study of complex systems due to its ability to classify binary
arrays of symbols according to their initial density. We show that a class of
modified GKL models over extended neighborhoods, but still involving only three
cells at a time, achieves comparable density classification performance but in
some cases reach consensus more than twice as fast. Our results suggest the
time to consensus (relative to the length of the CA) as a complementary measure
of density classification performance.Comment: Short note, 3 pages, 1 table, 2 composite figures, 18 reference