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

Francisco J. Muñoz () and Juan Carlos Nuño
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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

Mathematics, 2025, vol. 13, issue 16, 1-14

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.

Keywords: sequence generation; cellular automata with memory; de Bruijn sequences; shift registers; neural network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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