Software System Theory of the Forbidden Within Discrete Design

  • Iaakov ExmanEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 743)


Many “theoretical” frameworks have been proposed for software systems design with a plethora of techniques, scopes and degrees of sophistication. However, a clear delineation of the forbidden in software design terms is almost universally absent in all these frameworks. This absence is surprising, as other engineering disciplines obviously display forbidden regions. This paper claims that an acceptable software design theory should clearly demarcate the forbidden in contrast to the possible. Algebra is argued to be the mathematical field appropriate to determine boundaries of forbidden regions. To this end, a spectral approach is demonstrated, in which matrix eigenvectors play a central role. Such boundaries of forbidden regions are illustrated by a case study.


Software theory Forbidden regions Forbidden domains Boundary Algebra Eigenvectors Models Discrete software design Hierarchical software systems 


  1. 1.
    Abbot, J.J., Marayong, P., Okamura, A.M.: Haptic virtual fixtures for robot-assisted manipulation. In: Thrun, S., Brooks, R., Durrant-Whyte, H. (eds.) Robotics Research. Springer Tracts in Advanced Robotics, vol. 28, pp. 49–64. Springer, Berlin (2007). doi: 10.1007/978-3-540-48113-3_5CrossRefGoogle Scholar
  2. 2.
    Aneja, Y.P., Parlar, M.: Algorithms for weber facility location in the presence of forbidden regions and/or barriers to travel. Transp. Sci. 28(1), 70–76 (1994). doi: 10.1287/trsc.28.1.70CrossRefzbMATHGoogle Scholar
  3. 3.
    Brooks, F.P.: The Mythical Man-Month - Essays in Software Engineering – Anniversary. Addison-Wesley, Boston (1995)Google Scholar
  4. 4.
    Devadas, V., Aydin, H.: Real-time dynamic power management through device forbidden regions. In: Proceeding IEEE Real-Time and Embedded Technology and Applications Symposium, pp. 34–44 (2008). doi: 10.1109/RTAS.2008.21
  5. 5.
    Exman, I.: Linear software models, extended abstract. In: Jacobson, I., Goedicke, M., Johnson, P. (eds.) Proceeding. GTSE 2012, SEMAT Workshop on a General Theory of Software Engineering, pp. 23–24. KTH Royal Institute of Technology, Stockholm (2012)Google Scholar
  6. 6.
    Exman, I.: Linear Software Models, GTSE 2012, SEMAT Workshop on a General Theory of Software Engineering. KTH Royal Institute of Technology, Stockholm (2012). Video presentation of Ref. [5]:
  7. 7.
    Exman, I.: Linear software models: standard modularity highlights residual coupling. Int. J. Softw. Eng. Knowl. Eng. 24(2), 183–210 (2014). doi: 10.1142/S0218194014500089CrossRefGoogle Scholar
  8. 8.
    Exman, I.: Linear software models: decoupled modules from modularity matrix eigenvectors. Int. J. Softw. Eng. Knowl. Eng. 25(8), 1395–1426 (2015). doi: 10.1142/S0218194015500308CrossRefGoogle Scholar
  9. 9.
    Exman, I., Sakhnini, R.: Linear software models: modularity analysis by the Laplacian matrix. In: Proceeding 11th International Joint Conference on Software Technologies, ICSOFT-PT, vol. 2, pp. 100–108, Lisbon, Portugal (2016). doi: 10.5220/0005985601000108
  10. 10.
    Exman, I., Speicher, D.: Linear software models: equivalence of modularity matrix to its modularity lattice. In: Proceeding 10th ICSOFT International Joint Conference on Software Technologies, Colmar, France, pp. 109–116 (2015). doi: 10.5220/0005557701090116
  11. 11.
    Exman, I.: Software theory of the forbidden in a discrete design space. In: Proceeding 11th International Joint Conference on Software Technologies, ICSOFT-PT, vol. 2, pp. 131–137. Lisbon, Portugal, SciTePress (2016a). doi: 10.5220/0006004601310137
  12. 12.
    Exman, I.: The modularity matrix as a source of software conceptual integrity. In: Proceeding SKY 2016 - 7th International Workshop on Software Knowledge, Porto, Portugal, pp. 27–35. SciTePress (2016b)Google Scholar
  13. 13.
    Gamma, E., Helm, R., Johnson, R., Vlissides, J.: Design Patterns. Addison-Wesley, Boston (1995)zbMATHGoogle Scholar
  14. 14.
    Jackson, D.: Conceptual design of software: a research agenda. CSAIL Technical report, MIT-CSAIL-TR-2013-020 (2013).
  15. 15.
    Li, X.-Y., Guo, L.: Constructing affinity matrix in spectral clustering based on neighbor propagation. Neurocomputing 97, 125–130 (2012). doi: 10.1016/j.neucom.2012.06.023CrossRefGoogle Scholar
  16. 16.
    Messiah, A.: Quantum Mechanics, vol. I. North-Holland Publishing Co., Amsterdam (1961). Chap. III, Reprinted by Dover Publications (2014)zbMATHGoogle Scholar
  17. 17.
    Payandeh, S., Stanisic, Z.: On application of virtual fixtures as an aid for telemanipulation and training. In: Proceeding HAPTICS 2002 10th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, pp. 18–23 (2002). doi: 10.1109/HAPTIC.2002.998936
  18. 18.
  19. 19.
    Simon, H.A.: The Sciences of the Artificial, 3rd edn. MIT Press, Cambridge (1996)Google Scholar
  20. 20.
  21. 21.
    Slinky, Wave Phase changes at fixed end (2016b).
  22. 22.
    Standing wave (2016a). Standing_wave_2.gif
  23. 23.
    Standing wave, Standing waves on a Slinky (2016b).
  24. 24.
    Sullivan, K.J., Griswold, W.G., Cai, Y., Hallen, B.: The structure and value of modularity in software design. In: Proceeding ESEC/FSE 8th European Software Engineering Conference and 9th SIGSOFT International Symposium Foundations Software Engineering, pp. 99–108. ACM (2001). doi: 10.1145/503209.503224
  25. 25.
    UML, Specification, OMG (Object Management Group) (2015).
  26. 26.
    Weisstein, E.W.: Laplacian Matrix, From Mathworld–A Wolfram Web Resource (2016).
  27. 27.
    Wu, Y., Patel, J.M., Jagadish, H.V.: Estimating answer sizes for XML queries. In: Jensen, C.S. et al. (ed.) EDBT 2002. LNCS, vol. 2287, pp. 590–608. Springer, Heidelberg (2002). doi: 10.1007/3-540-45876-X_37CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Software Engineering DepartmentThe Jerusalem College of Engineering – JCE - AzrieliJerusalemIsrael

Personalised recommendations