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Designing and modeling cyberworlds using the incrementally modular abstraction hierarchy based on homotopy theory

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Abstract

For designing and modeling complicated and sophisticated systems such as cyberworlds, their mathematical foundation is critical. To realize it, two important properties called the homotopy lifting property (HLP) and homotopy extension property (HEP) are applied for designing and modeling a system in a bottom-up way and a top-down way, respectively. In this paper, an enterprise system and a real-time embedded system are considered as important socially emerging cases of cyberworlds, where the π-calculus processes for describing these behaviors formally, a Petri net for explaining process interactions, and XMOS XC programs are modeled and designed by our approach. The spaces in both properties are specified by the incrementally modular abstraction hierarchy by climbing down the abstraction hierarchy from the most abstract homotopy level to the most specific view level, while keeping invariants such as homotopy equivalence and topological equivalence.

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References

  1. Havey, M.: Essential Business Process Modeling. O’Reilly Media, Cambridge (2005)

    Google Scholar 

  2. Hennessy, M.: A Distributed Pi-Calculus. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  3. Kunii, T.L.: Cyberworlds—Theory, design and potetial. Trans. Inst. Electron. Inf. Commun. Eng. E88-D(5), 790–800 (2005)

    Google Scholar 

  4. Kunii, T.L., Ohmori, K.: Cyberworlds: Architecture and modeling by an incrementally modular abstraction hierarchy. Vis. Comput. 22(12), 949–964 (2006)

    Article  Google Scholar 

  5. May, D.: Communicating process architecture for multicores. In: The 30th Communicating Process Architectures Conference, pp. 21–32 (2007)

  6. Milner, R.: Communicating and Mobile Systems: Pi-Calculus. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  7. Ohmori, K., Kunii, T.L.: An incrementally modular abstraction hierarchy for linear software development methodology. In: Int. Conf. on Cyberworlds 2006, pp. 216–223 (2006)

  8. Ohmori, K., Kunii, T.L.: Development of an accounting system. In: ICEIS2007, pp. 437–444 (2007)

  9. Ohmori, K., Kunii, T.L.: The mathematical structure of cyberworlds. In: Int. Conf. on Cyberworlds 2007, pp. 100–107 (2007)

  10. Ohmori, K., Kunii, T.L.: Mathematical modeling of ubiquitous systems. In: Int. Conf. on Cyberworlds 2008, pp. 69–74 (2008)

  11. Ohmori, K., Kunii, T.L.: A pi-calculus modeling method for cyberworlds systems using the duality between a fibration and a cofibration. In: Int. Conf. on Cyberworlds 2008, pp. 363–370 (2008)

  12. Ohmori, K., Kunii, T.L.: Mathematical foundation for designing and modeling cybeworlds. In: Int. Conf. on Cyberworlds 2009, pp. 80–87 (2009)

  13. Pierce, B.C., Turner, D.N.: Pict: A programming language based on the pi-calculus. Indiana University CSCI Technical Report 476, pp. 1–26 (1997)

  14. Sangiorgi, D., Walker, D.: The Pi-Calculus: A Theory of Mobile Processes. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  15. Sieradski, A.J.: An Introduction to Topology and Homotopy. PWS-Kent, Boston (1992)

    MATH  Google Scholar 

  16. Spanier, E.H.: Algebraic Topology. Springer, New York (1966)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Hosei University, 3-7-2 Kajinocho, Koganei-shi, Tokyo, 184-8584, Japan

    Kenji Ohmori

  2. Morpho, Inc., University of Tokyo, Entrepreneur Plaza 5F, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Tosiyasu L. Kunii

Authors
  1. Kenji Ohmori
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  2. Tosiyasu L. Kunii
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Correspondence to Kenji Ohmori.

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Ohmori, K., Kunii, T.L. Designing and modeling cyberworlds using the incrementally modular abstraction hierarchy based on homotopy theory. Vis Comput 26, 297–309 (2010). https://doi.org/10.1007/s00371-010-0420-7

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