Modelling Memory Requirement with Normal Symbolic Form

  • Marc Csernel
  • Francisco A. T. de Carvalho
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Symbolic objects can deal with domain knowledge expressed by dependency rules between variables. However taking into account this rules in order to analyze symbolic data can lead to exponential computation time. It’s why we introduced an approach called Normal Symbolic Form (NSF) which lead to a polynomial computation time, but may sometimes bring about an exponential explosion of space memory requirement. In a previous paper we studied this possible memory requirement and we saw how it is bounded according to the nature of the variables and rules. The aim of this paper is to model this memory space requirement. The proposed modelling of this problem is related to the Maxwell-Boltzmann statistics currently used on thermodynamics.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. BOCK, H.-H. and DIDAY, E. (2000): Analysis of Symbolic Data. Springer, Berlin.CrossRefGoogle Scholar
  2. CODD, E.E. (1972): Further Normalization of the Data Relational Model. In: R. Rustin (Ed.): Data Base Systems. Prentice-Hall, Englewood Cliffs, N.J., 33–64.Google Scholar
  3. CSERNEL, M. (1998): On the Complexity of Computation with Symbolic Objects using Domain Knowledge. In: A. Rizzi, M. Vichi, and H.-H. Bock (Eds.): Advances in Data Science and Classification. Springer, Heidelberg, 403–408.CrossRefGoogle Scholar
  4. CSERNEL, M. and DE CARVALHO, F. A. T. (2002): On memory requirement with Normal Symbolic Form. In: O. Opitz and M. Schwaiger (Eds.): Exploratory Data Analysis in Empirical Research. Springer, Heidelberg (accepted to be published)Google Scholar
  5. CSERNEL, M. and DE CARVALHO, F. A. T. (1999): Usual Operations with Symbolic Data under Normal Symbolic Form. Applied Stochastic Models in Business and Industry, 15, 241–257.zbMATHCrossRefGoogle Scholar
  6. DE CARVALHO, F. A. T. (1998): Extension based Proximities between Constrained Boolean Symbolic Objects. In: Hayashi, Ohsumi, Yajima, Tanaka, Bock, Baba (Eds.): Data Science, Classification and Related Methods. Springer, Berlin, 370–378.Google Scholar
  7. VIGNES, R. (1991): Caractérisation Automatique de Groupes Biologiques. Thèse de Doctorat. Université Paris VI, Paris.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marc Csernel
    • 1
  • Francisco A. T. de Carvalho
    • 2
  1. 1.Rocquencourt, Domaine de Voluceau — RocquencourtINRIALe Chesnay CedexFrance
  2. 2.Centro de Informatica — CIn / UFPERecifeBrasil

Personalised recommendations