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2015•arXiv (Cornell University)Open access

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

Shalosh B. Ekhad, Neil J.A. Sloane, Doron Zeilberger

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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.

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What this paper is about

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.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Modulo, Logarithm, Prime (order theory), Algorithm, Polynomial, Discrete mathematics, Mathematics, Primitive root modulo n

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