Solution of the density classification problem with two cellular automata rules
Abstract
Recently, Land and Belew [Phys. Rev. Lett. 74, 5148 (1995)] have shown that no onedimensional twostate cellular automaton which classifies binary strings according to their densities of 1's and 0's can be constructed. We show that a pair of elementary rules, namely the ``traffic rule'' 184 and the ``majority rule'' 232, performs the task perfectly. This solution employs the second order phase transition between the freely moving phase and the jammed phase occurring in rule 184. We present exact calculations of the order parameter in this transition using the method of preimage counting.
 Publication:

Physical Review E
 Pub Date:
 March 1997
 DOI:
 10.1103/PhysRevE.55.R2081
 arXiv:
 arXiv:compgas/9703001
 Bibcode:
 1997PhRvE..55.2081F
 Keywords:

 Nonlinear Sciences  Cellular Automata and Lattice Gases
 EPrint:
 4 pages (RevTeX), 1 figure