%0 Conference Proceedings
%T Restricted Density Classification in One Dimension
%+ Universiteit Leiden = Leiden University 
%A Taati, Siamak
%Z Part 2: Regular Papers
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA)
%C Turku, Finland
%Y Jarkko Kari
%3 Cellular Automata and Discrete Complex Systems
%V LNCS-9099
%P 238-250
%8 2015-06-08
%D 2015
%R 10.1007/978-3-662-47221-7_18
%K Cellular automata
%K Density classification
%K Phase transition
%K Spareness
%K Percolation
%Z Computer Science [cs]Conference papers
%X The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It is not known whether a one-dimensional cellular automaton with binary alphabet can classify all Bernoulli random configurations almost surely according to their densities. We show that any cellular automaton that washes out finite islands in linear time classifies all Bernoulli random configurations with parameters close to <strong>0</strong> or <strong>1</strong> almost surely correctly. The proof is a direct application of a “percolation” argument which goes back to Gács (1986).
%G English
%Z TC 1
%Z WG 1.5
%2 https://inria.hal.science/hal-01442476/document
%2 https://inria.hal.science/hal-01442476/file/338243_1_En_18_Chapter.pdf
%L hal-01442476
%U https://inria.hal.science/hal-01442476
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-LNCS-9099
%~ IFIP-WG1-5
%~ IFIP-AUTOMATA