The Pagoda Sequence: a Ramble through Linear Complexity, Number Walls, D0L Sequences, Finite State Automata, and Aperiodic Tilings

Fred Lunnon

We review the concept of the number wall as an alternative to the traditional linear complexity profile (LCP), and sketch the relationship to other topics such as linear feedback shift-register (LFSR) and context-free Lindenmayer (D0L) sequences. A remarkable ternary analogue of the Thue-Morse sequence is introduced having deficiency 2 modulo 3, and this property verified via the re-interpretation of the number wall as an aperiodic plane tiling.

In Turlough Neary, Damien Woods, Tony Seda and Niall Murphy: Proceedings International Workshop on The Complexity of Simple Programs (CSP 2008), Cork, Ireland, 6-7th December 2008, Electronic Proceedings in Theoretical Computer Science 1, pp. 130–148.
Published: 25th June 2009.

ArXived at: bibtex PDF

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