We present an extension of Kleene algebra (KA) that can be used for modeling a record based view of pointer structures. This is achieved by transferring some concepts of fuzzy relation theory to KAs. The defined framework enables us to maintain within a single extended Kleene algebra several equally shaped KAs modeling distinct record selectors.


Kleene algebra embedding pointer algebra pointer structures 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Clenaghan, K.: Calculational graph algorithmics: reconciling two approaches with dynamic algebra. Technical report CS-R9518, CWI - Centrum voor Wiskunde en Informatica (March 1995)Google Scholar
  2. 2.
    Cohen, E.: Separation and reduction. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837, pp. 45–59. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Conway, J.H.: Regular Algebra and Finite Machines. Chapman & Hall, London (1971)zbMATHGoogle Scholar
  4. 4.
    Desharnais, J., Möller, B., Struth, G.: Kleene algebra with a domain operator. Technical report 2003-7, Institut für Informatik, Universität Augsburg (2003)Google Scholar
  5. 5.
    Desharnais, J., Möller, B., Tchier, F.: Kleene under a Demonic Star. In: Rus, T. (ed.) AMAST 2000. LNCS, vol. 1816, pp. 355–370. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Ehm, T.: Properties of overwriting for updates in typed Kleene algebras. Technical report 2000-7, Institut für Informatik, Universität Augsburg (2000)Google Scholar
  7. 7.
    Ehm, T.: Transformational Construction of Correct Pointer Algorithms. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds.) PSI 2001. LNCS, vol. 2244, pp. 116–130. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Ehm, T.: The Kleene Algebra of Nested Pointer Structures: Theory and Applications. PhD thesis, Universität Augsburg (2003)Google Scholar
  9. 9.
    Ehm, T., Möller, B., Struth, G.: Kleene modules. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2003. LNCS, vol. 3051, Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Freyd, P.J., Scedrov, A.: Categories, Allegories. North-Holland Mathematical Library, vol. 39. North-Holland, Amsterdam (1990)zbMATHGoogle Scholar
  11. 11.
    Hoare, C.A.R., Jifeng, H.: A trace model for pointers and objects. In: Guerraoui, R. (ed.) ECOOP 1999. LNCS, vol. 1628, pp. 1–17. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Kawahara, Y., Furusawa, H.: Crispness and representation theorems in Dedekind categories. Technical report DOI-TR 143, Kyushu University (1997)Google Scholar
  13. 13.
    Kozen, D.: Kleene algebra with tests. ACM Transactions on Programming Languages and Systems 19(3), 427–443 (1997)CrossRefGoogle Scholar
  14. 14.
    Möller, B.: Calculating with pointer structures. In: Bird, R., Meertens, L. (eds.) Algorithmic Languages and Calculi, Proc. IFIP TC2/WG2.1 Working Conference, Le Bischenberg, February 1997, pp. 24–48. Chapman & Hall, Boca Raton (1997)Google Scholar
  15. 15.
    Pratt, V.: Action logic and pure induction. In: van Benthem, J., Eijck, J. (eds.) Proceedings of JELIA 1990, European Workshop on Logics in AI, Amsterdam (September 1990)Google Scholar
  16. 16.
    Pratt, V.: Dynamic Algebras as a well-behaved fragment of Relation Algebras. In: Bergman, C.H., Pigozzi, D.L., Maddux, R.D. (eds.) Algebraic Logic and Universal Algebra in Computer Science. LNCS, vol. 425, Springer, Heidelberg (1990)CrossRefGoogle Scholar
  17. 17.
    von Wright, J.: From Kleene algebra to refinement algebra. In: Boiten, E.A., Möller, B. (eds.) MPC 2002. LNCS, vol. 2386, pp. 233–262. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Winter, M.: Relational constructions in Goguen categories. In: de Swart, H. (ed.) 6th International Seminar on Relational Methods in Computer Science (RelMiCS), pp. 222–236 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thorsten Ehm
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany

Personalised recommendations