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Hilbert words as arrays generated with P systems

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Abstract

Construction of finite grammars to generate languages of digitized picture patterns, considered as arrays of symbols, has been a problem of interest in two-dimensional formal languages. On the other hand, in the area of membrane computing, P systems were developed for handling the problem of picture array generation, with the rewriting involved being sequential or parallel. We introduce in this paper the array representation for the Hilbert words, the finite approximations of the Hilbert space-filling curve, and we generate them with array-rewriting rules in P systems. The array rewriting is done in parallel, with the P system serving as a control mechanism. A main contribution is the proof of correctness which is done using a linearization procedure. In addition, the advantage of the P system used is that the number of membranes involved is small (only one or two).

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Acknowledgements

An earlier version of this work was presented at ACMC 2019, 14-16 November 2019, Xiamen, China. The work of RC and LZ was supported by the National Natural Science Foundation of China (61772214). The work of GZ was supported by the National Natural Science Foundation of China (61972324) and by Sichuan Science and Technology Program (2021YFS0313, 2021YFG0133). The authors are greatly indebted to the reviewers for their comments and suggestions, which led to improvements, and resulted in the present form of the paper.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei St 14, 010014, Bucharest, Romania

    Rodica Ceterchi

  2. Key Laboratory of Image Information Processing and Intelligent Control of Education Ministry of China, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Luping Zhang

  3. Faculty of Science, Liverpool Hope University, Hope Park, Liverpool, L16 9JD, UK

    K. G. Subramanian

  4. School of Control Engineering, Chengdu University of Information Technology, Chengdu, 610225, China

    Gexiang Zhang

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  1. Rodica Ceterchi
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  2. Luping Zhang
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  3. K. G. Subramanian
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  4. Gexiang Zhang
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Correspondence to Luping Zhang.

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In Memoriam Professor Rani Siromoney.

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Ceterchi, R., Zhang, L., Subramanian, K.G. et al. Hilbert words as arrays generated with P systems. J Membr Comput 3, 163–169 (2021). https://doi.org/10.1007/s41965-021-00078-y

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