Simple cellular automata as pseudorandom m-sequence generators for built-in self-test

Authors:
Makoto Matsumoto
Affiliations:
Keio Univ., Yokohama, Japan/ and Max-Plank-Institut fü/r Mathematik
Venue:
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Year:
1998

Citing 2
Cited 1

Parallel Random Number Generation for VLSI Systems Using Cellular Automata

IEEE Transactions on Computers
Theory of Self-Reproducing Automata

Theory of Self-Reproducing Automata

Pseudorandom number generation based on controllable cellular automata

Future Generation Computer Systems - Special issue: Advanced services for clusters and internet computing

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Abstract

We propose an extremely simple and explicit construction of cellular automata (CA) generating pseudorandom m-sequences, which consist of only one type of cells. This construction has advantages over the previous researches in the following points. (1) There is no need to search for primitive polynomials; a simple sufficient number-theoretic condition realizes maximal periodic CA with periods 2m− 1, m =2, 3, 5, 89, 9689, 21701, 859433. (2) The configuration does not require hybrid constructions. This makes the implementation much easier. This is a modification of the Rule-90 by Wolfram. We list our CAs with maximal period, up to the size 300. We also discuss the controllability of the CA, randomness of the generated sequence, and a two-dimensional version.