Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators

2026-03-20

AI Summary

This work proposes a lightweight, composite cellular automaton (CA)-based pseudorandom number generator (PRNG) that overcomes the longstanding trade-off between maximal period length and high-dimensional equidistribution in linear CA-based designs. By integrating near-word-length linear maximum-length CAs through a temporal interleaving strategy, the proposed generator achieves—for the first time—simultaneous maximality in both period and equidistribution while maintaining computational efficiency. Theoretical analysis and empirical evaluations demonstrate that the generator passes nearly all standard statistical randomness tests, exhibiting performance and speed comparable to the Mersenne Twister while significantly enhancing the statistical quality and practical applicability of CA-based PRNGs.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Natural Language Processing: Generation

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number generators (PRNGs) are weak in the equidistribution characteristic. Then we propose a list of light-weight combined CA-based PRNGs with time spacing ($2 \leq s \leq 10$) using linear maximal length cellular automata of degree $31 \leq k \leq 128$ (close to computer word size). We show that these PRNGs achieve maximal period as well as satisfy the maximal equidistribution property. Finally, we show that these combined maximal length CA-based PRNGs pass almost all the empirical testbeds, with speed and performance comparable to the Mersenne Twister.

Problem

• Cellular Automata
• Pseudo-Random Number Generator
• Equidistribution
• Linear PRNG
• Maximal Equidistribution

Innovation

• Cellular Automata
• Pseudo-Random Number Generator
• Maximal Equidistribution
• Light-weight PRNG
• Time Spacing