Subword Balance in BinaryWords, Languages and Sequences

Authors:
Arto Salomaa
Affiliations:
Turku Centre for Computer Science, Joukahaisenkatu 3-5 B, 20520 Turku, Finland. E-mail: asalomaa@utu.fi
Venue:
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Year:
2007

Citing 13
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Extending Parikh matrices

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Subword histories and Parikh matrices

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Reconstruction from subsequences

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Some characterizations of Parikh matrix equivalent binary words

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Connections between subwords and certain matrix mappings

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On the Injectivity of Parikh Matrix Mappings

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Abstract

We investigate binary words and languages having a balanced structure of (scattered) subwords. We introduce a "difference function" D for binary words. For D=0, the resulting language is properly context-sensitive. Parikh matrices constitute a useful technical tool in the study, we investigate also the independence of their entries. The investigation is extended to concern ω-words and periodicity. For the Fibonacci word, the D-values are in many ways connected with the Fibonacci numbers.