A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata

Abstract

We develop a meta-algorithm that, given a polynomial (in one or more variables), and a prime p, produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears as a coefficient when the polynomial is raised to the power n and the coefficients are read modulo p.Comment: 8 pages, accompanied by a Maple package, and numerous input and output files that can be gotten from http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/CAcount.htm