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An Overview of 2D Picture Array Generating Models Based on Membrane Computing

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Reversibility and Universality

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 30))

Abstract

A variety of two-dimensional array grammar models generating picture array languages have been introduced and investigated, utilizing and extending the well-established notions and techniques of formal string language theory. On the other hand the versatile computing model with a generic name of P system in the area of membrane computing, has turned out to be a rich framework for different kinds of problems in a variety of fields. Picture array generation in the field of two-dimensional (2D) languages is one such area where P systems with array objects and array rewriting, referred to as array P systems, have been fruitfully employed in increasing the generating power of the 2D grammar models. A variety of array P systems have been proposed in the literature. The objective of this survey is to review and describe the salient features of the major types of array P systems, which have served as the basis for developing other kinds of array P systems. Applications of these array P systems are also briefly described besides indicating possible new directions of investigation.

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Acknowledgements

The authors are grateful to Prof. Andrew Adamatzky for extending the authors a valuable opportunity to have this paper in a volume celebrating the life-time achievements of Prof. Kenichi Morita, a wonderful researcher with great contributions in many areas including two-dimensional languages. The authors thank the referees for their very useful comments which enabled them to provide a better presentation. The work was supported by National Natural Science Foundation of China (61320106005, 61602192, and 61772214), China Postdoctoral Science Foundation (2016M600592 and 2017T100554). The first and second authors, K.G. Subramanian and Sastha Sriram, gratefully acknowledge the support extended to them by Prof. Linqiang Pan for an academic visit to Huazhong University of Science and Technology, Wuhan, China from May 03, 2017 to June 02, 2017, where part of this research was done.

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Authors and Affiliations

  1. Honorary Visiting Professor (March 2017–February 2021), Department of Mathematics and Computer Science, Faculty of Science, Liverpool Hope University, Liverpool, L16 9JD, UK

    K. G. Subramanian

  2. Department of Mathematics, KL University, Vaddeswaram, Guntur, 522502, Andhra Pradesh, India

    Sastha Sriram

  3. School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Bosheng Song & Linqiang Pan

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  1. K. G. Subramanian
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  2. Sastha Sriram
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  3. Bosheng Song
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  4. Linqiang Pan
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Correspondence to Linqiang Pan .

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  1. Unconventional Computing Centre, University of the West of England, Bristol, United Kingdom

    Andrew Adamatzky

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Subramanian, K.G., Sriram, S., Song, B., Pan, L. (2018). An Overview of 2D Picture Array Generating Models Based on Membrane Computing. In: Adamatzky, A. (eds) Reversibility and Universality. Emergence, Complexity and Computation, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-73216-9_16

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  • DOI: https://doi.org/10.1007/978-3-319-73216-9_16

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