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Relational semantics for locally nondeterministic programs

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Abstract

Introducing nondeterministic operators in a conventional deterministic language gives rise to various semantic difficulties. One of the problems is that there has been no semantic domain that is wholly satisfactory for denoting nondeterministic programs.

In this paper, we propose an approach based on relational algebra. We divide the semantics of a nondeterministic program into two parts. The first part concerns the angelic aspect of programs and the second part concerns the demonic aspect of programs. Because each semantic function used in these parts is monotonic with respect to an ordering on relations, the existence of the fixed points of recursively defined nondeterministic programs is ensured.

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Author information

Authors and Affiliations

  1. Mathematical Systems Institute Inc., 10F FOUR SEASONS BLDG., 2-4-3 Shinjuku, Shinjuku-ku, Tokyo, Japan

    Liangwei Xu

  2. Department of Mathematical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan

    Masato Takeichi

  3. Faculty of Technology, Tokyo University of Agriculture and Technology, 2-24-16 Naka-chou, Koganei-shi, Tokyo, Japan

    Hideya Iwasaki

Authors
  1. Liangwei Xu
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  2. Masato Takeichi
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  3. Hideya Iwasaki
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Additional information

Liangwei Xu: His research interests are computational model, program transformation and derivation methodology. He received the B. E. degree from Shanghai Jiao Tong University in 1982 and the M.E. degree from University of Tokyo in 1992. He currently joins Mathematical Systems Institute Inc.

Masato Takeichi, Dr. Eng.: He is a Professor of Department of Mathematical Engineering. Graduate School of Engineering, University of Tokyo. His research interests are functional programming, language implementation and constructive algorithmics.

Hideya Iwasaki, Dr. Eng.: He is an Associate Professor of Faculty of Technology, Tokyo University of Agriculture and Technology. He received the M.E. degree in 1985, the Dr. Eng. degree in 1988 from University of Tokyo. His research interests are list processing languages, functional languages, parallel processing, and constructive algorithmics.

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Xu, L., Takeichi, M. & Iwasaki, H. Relational semantics for locally nondeterministic programs. New Gener Comput 15, 339–361 (1997). https://doi.org/10.1007/BF03037950

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  • DOI: https://doi.org/10.1007/BF03037950

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