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HyperLMNtal: An Extension of a Hierarchical Graph Rewriting Model

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Abstract

LMNtal (pronounced “elemental”) is a language model based on hierarchical graph rewriting that uses point-to-point links to represent connectivity and membranes to represent hierarchy. LMNtal was designed to be a substrate language of various computational models, especially those addressing concurrency, mobility and multiset rewriting.

Although point-to-point links and membranes could be used together to represent multipoint connectivity, our experiences with LMNtal showed that hyperlinks would be an important and useful extension to the language.

We have accordingly expanded LMNtal into a hierarchical hypergraph rewriting language model, HyperLMNtal. HyperLMNtal enabled concise description of computational models involving flexible and diverse forms of references between data; in particular, it enabled efficient encoding of a constraint processing language CHR in terms of both performance and computational complexity.

This paper describes the design and implementation of HyperLMNtal as a case study of language evolution.

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Notes

  1. http://www.ueda.info.waseda.ac.jp/lmntal/

  2. http://people.cs.kuleuven.be/~tom.schrijvers/Research/CHR/

  3. A rule can be prefixed by a rule name and ‘@@’.

  4. The guard constraint =:= checks integer equality.

  5. A syntactic sugar, inspired by CHR’s sympagation rule, allows us to write a rule T 1,T 2   :-   T 1,T 3 as T 1\T 2   :-   T 3.

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Acknowledgements

The authors are indebted to the present and past members of the LMNtal group for fruitful discussions and for building the LMNtal system on which the present work was successfully based. They would like to thank anonymous referees for their careful reviewing and useful comments.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Kazunori Ueda & Seiji Ogawa

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  1. Kazunori Ueda
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  2. Seiji Ogawa
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Correspondence to Kazunori Ueda.

Additional information

Partially supported by Grant-In-Aid for Scientific Research ((B) 23300011), JSPS, Japan.

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Ueda, K., Ogawa, S. HyperLMNtal: An Extension of a Hierarchical Graph Rewriting Model. Künstl Intell 26, 27–36 (2012). https://doi.org/10.1007/s13218-011-0162-3

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