Rule-based Generation of de Bruijn Sequences: Memory and Learning
Year: 2025
Type: preprint
Abstract: We investigate binary sequences generated by non-Markovian rules with memory length $μ$, similar to those adopted in Elementary Cellular Automata. This generation procedure is equivalente to a shift register and certain rules produce sequences with maximal periods, known as de Bruijn sequences. We introduce a novel methodology for generating de Bruijn sequences that combines: (i) a set of derived properties that significantly reduce the space of feasible generating rules, and (ii) a neural network-based classifier that identifies which rules produce de Bruijn sequences. Experiments for large values of $μ$ demonstrate the approach's effectiveness and computational efficiency.
Source: arXiv (Cornell University)
Authors: Muñoz, Francisco J., Nuño, Juan Carlos
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891847950
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