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.
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