3 research outputs found
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
An asynchronous two-dimensional self-correcting cellular automaton
Annual Symposium on Foundations of Computer Science (Proceedings)278-285ASFP
Reliable Cellular Automata with Self-Organization
In a probabilistic cellular automaton in which all local transitions have
positive probability, the problem of keeping a bit of information indefinitely
is nontrivial, even in an infinite automaton. Still, there is a solution in 2
dimensions, and this solution can be used to construct a simple 3-dimensional
discrete-time universal fault-tolerant cellular automaton. This technique does
not help much to solve the following problems: remembering a bit of information
in 1 dimension; computing in dimensions lower than 3; computing in any
dimension with non-synchronized transitions.
Our more complex technique organizes the cells in blocks that perform a
reliable simulation of a second (generalized) cellular automaton. The cells of
the latter automaton are also organized in blocks, simulating even more
reliably a third automaton, etc. Since all this (a possibly infinite hierarchy)
is organized in ``software'', it must be under repair all the time from damage
caused by errors. A large part of the problem is essentially self-stabilization
recovering from a mess of arbitrary size and content. The present paper
constructs an asynchronous one-dimensional fault-tolerant cellular automaton,
with the further feature of ``self-organization''. The latter means that unless
a large amount of input information must be given, the initial configuration
can be chosen homogeneous.Comment: 166 pages, 17 figure