An analytical formulation for cellular automata (CA) based solution of density classification task (DCT)

Authors:
Nirmalya Sundar Maiti;Shiladitya Munshi;P. Pal Chaudhuri
Affiliations:
Cellular Automata Research Lab (CARL), India;Cellular Automata Research Lab (CARL), India;Cellular Automata Research Lab (CARL), India
Venue:
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
Year:
2006

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Abstract

This paper presents an analytical solution for Density Classification Task (DCT) with an n cell inhomogeneous Cellular Automata represented by its Rule Vector (RV) R0R1R2 ⋯Ri ⋯Rn−−1, where rule Ri is employed on ith cell (i=0,1,2,⋯(n-1)) It reports the Best Rule Vector (BRV) for solution of DCT The concept of Rule Vector Graph (RVG) has provided the framwork for the solution RVG derived from the RV of a CA can be analyzed to derive the Best Rule Vector (BRV) consisting of only rule 232 and 184 (or 226) for 3-neighborhood CA and their equivalent rules for k-neighborhood CA (k3) The error analysis of the solution has been also reported.