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Decidability on Dube’s Self-similar Fractals

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Book cover Artificial Intelligence and Computational Intelligence (AICI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7003))

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Abstract

Dube proved some undecidability on self-affine fractals. In this paper, we obtain the decidability for self-similar fractal of Dube’s type. In fact, we prove that the following problems are decidable to test if the Hausdorff dimension of a given Dube’s self-similar set is equal to its similarity dimension, and to test if a given Dube’s self-similar set satisfies the strong separation condition.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, Zhejiang Wanli University, Ningbo, 315100, China

    Qin Wang

  2. Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, China

    Lifeng Xi

Authors
  1. Qin Wang
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  2. Lifeng Xi
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Editor information

Editors and Affiliations

  1. School of Business Information Technology, RMIT University, City Campus, 124 La Trobe Street, 3000, Melbourne, VIC, Australia

    Hepu Deng

  2. School of Electronics and Information, Tongji University, 201804, Shanghai, China

    Duoqian Miao

  3. School of Computer and Information Engineering, Shanghai University of Electric Power, 200090, Shanghai, China

    Jingsheng Lei

  4. Department of Business Administration, Caritas Institute of Higher Education, 18 Chui Ling Road, Tseung Kwan O, Hong Kong, China

    Fu Lee Wang

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© 2011 Springer-Verlag Berlin Heidelberg

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Wang, Q., Xi, L. (2011). Decidability on Dube’s Self-similar Fractals. In: Deng, H., Miao, D., Lei, J., Wang, F.L. (eds) Artificial Intelligence and Computational Intelligence. AICI 2011. Lecture Notes in Computer Science(), vol 7003. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23887-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-23887-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23886-4

  • Online ISBN: 978-3-642-23887-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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