ENTERPRISE SYSTEM DEVELOPMENT WITH INVARIANT PRESERVING - A Mathematical Approach by the Homotopy Lifting and Extension Properties

Kenji Ohmori, Tosiyasu L. Kunii

Abstract

In this paper, a theoretical method for developing enterprise systems represented by the π-calculus is introduced. The method is based on the modern mathematics of homotopy theory. The homotopy lifting and extension properties are applied to developing systems in bottom-up and top-down ways with the incrementally modular abstraction hierarchy, where system development is carried out by climbing down abstraction hierarchy with adding invariants linearly. It leads to avoid combinatorial explosions causing an enormous waste of time and cost on testing. The system requirements and a state transition diagram drive the actions of an event by applying the HEP. Then, the state transition diagram and actions bring π-calculus processes by applying the HLP. These processes do not need testing because of invariant preserving.

References

  1. Havey, M. (2005). Essential Business Process Modeling. O'Reilly Media, Inc, Cambridge.
  2. Hennessy, M. (2001). A Distributed Pi-Calculus. Cambridge University Press, Cambridge.
  3. Kunii, T. L. (2005).
  4. potetial-. The Transactions of The Institute of Electronics, Information and Communication Engineers, E88-D(5):790-800.
  5. Kunii, T. L. and Ohmori, K. (2006). Cyberworlds: Architecture and modeling by an incrementally modular abstraction hierarchy. The Visual Computer, 22(12):949-964.
  6. Milner, R. (1999). Communicating And Mobile Systems: Pi-Calculus. Cambridge University Press, Cambridge.
  7. Ohmori, K. and Kunii, T. L. (2006). An incrementally modular abstraction hierarchy for linear software development methodology. Int. Conf. on Cyberworlds 2006, pages 216-223.
  8. Ohmori, K. and Kunii, T. L. (2007a). Development of an accounting system. ICEIS2007, pages 437-444.
  9. Ohmori, K. and Kunii, T. L. (2007b). The mathematical structure of cyberworlds. Int. Conf. on Cyberworlds 2007, pages 100-107.
  10. Ohmori, K. and Kunii, T. L. (2008a). Mathematical modeling of ubiquitous systems. Int. Conf. on Cyberworlds 2008, pages 69-74.
  11. Ohmori, K. and Kunii, T. L. (2008b). A pi-calculus modeling method for cyberworlds systems using the duality between a fibration and a cofibration. Int. Conf. on Cyberworlds 2008, pages 363-370.
  12. Sangiorgi, D. and Walker, D. (1999). The Pi-Calculus: A Theory of Mobile Processes. Cambridge University Press, Cambridge.
  13. Sieradski, A. J. (1992). An introduction to topology and homotopy. PWS-Kent Publishing Company, Boston.
  14. Spanier, E. H. (1966). Algebraic topology. Springer-Verlag, New York.
Download


Paper Citation


in Harvard Style

Ohmori K. and L. Kunii T. (2009). ENTERPRISE SYSTEM DEVELOPMENT WITH INVARIANT PRESERVING - A Mathematical Approach by the Homotopy Lifting and Extension Properties . In Proceedings of the 11th International Conference on Enterprise Information Systems - Volume 3: ICEIS, ISBN 978-989-8111-86-9, pages 116-123. DOI: 10.5220/0001981501160123


in Bibtex Style

@conference{iceis09,
author={Kenji Ohmori and Tosiyasu L. Kunii},
title={ENTERPRISE SYSTEM DEVELOPMENT WITH INVARIANT PRESERVING - A Mathematical Approach by the Homotopy Lifting and Extension Properties},
booktitle={Proceedings of the 11th International Conference on Enterprise Information Systems - Volume 3: ICEIS,},
year={2009},
pages={116-123},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001981501160123},
isbn={978-989-8111-86-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th International Conference on Enterprise Information Systems - Volume 3: ICEIS,
TI - ENTERPRISE SYSTEM DEVELOPMENT WITH INVARIANT PRESERVING - A Mathematical Approach by the Homotopy Lifting and Extension Properties
SN - 978-989-8111-86-9
AU - Ohmori K.
AU - L. Kunii T.
PY - 2009
SP - 116
EP - 123
DO - 10.5220/0001981501160123