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Rule-Based Generation of de Bruijn Sequences: Memory and Learning

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  • Francisco J. Muñoz

    (Departamento de Matemática Aplicada, Ciencia e Ingeniería de Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, Móstoles, 28933 Madrid, Spain)

  • Juan Carlos Nuño

    (Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain)

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 equivalent 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. The experiments for some values of μ demonstrate the approach’s effectiveness and computational efficiency.

Suggested Citation

  • Francisco J. Muñoz & Juan Carlos Nuño, 2025. "Rule-Based Generation of de Bruijn Sequences: Memory and Learning," Mathematics, MDPI, vol. 13(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2598-:d:1724030
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