Abstract
Cobham stated that sequences over a finite alphabet can be generated by anr-substitution if and only if they arer-automatic. Those sequences linked with automata as well as with substitutions may nevertheless possess sets of subwords which are, if interpreted as languages, not even context-free. This result is obtained by a study of the properties of paperfolding sequences. It is shown that any context-free set consisting of subwords of paperfolding sequences is finite.
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References
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Michel Mendès France and A. J. van der Poorten. Arithmetic and analytic properties of paperfolding sequences.Bulletin of the Australian Mathematical Society, 24: 123–131, 1981.
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Lehr, S. A result about languages concerning paperfolding sequences. Math. Systems Theory 25, 309–313 (1992). https://doi.org/10.1007/BF01213862
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DOI: https://doi.org/10.1007/BF01213862