Stochastic inference of regular tree languages

  • Rafael C. Carrasco
  • Jose Oncina
  • Jorge Calera
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1433)


We generalize a former algorithm for regular language identification from stochastic samples to the case of tree languages or, equivalently, string languages where structural information is available. We also describe a method to compute efficiently the relative entropy between the target grammar and the inferred one, useful for the evaluation of the inference.


Relative Entropy Regular Language Tree Language Stochastic Sample Grammatical Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aho, A.V. & Ullman, J.D. (1972): “The theory of parsing, translation and compiling. Volume I: Parsing”. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  2. Angluin, D. (1982): Inference of reversible languages. Journal of the Association for Computing Machines 29, 741–765.zbMATHMathSciNetGoogle Scholar
  3. Calera, J. & Carrasco, R.C: (1998): Computing the relative entropy between regular tree languages. Submitted for publication.Google Scholar
  4. Carrasco, R.C. (1997): “Inferencia de lenguajes rationales estocásticos”. Ph.D. dissertation. Universidad de Alicante.Google Scholar
  5. Carrasco, R.C. (1998): Accurate computation of the relative entropy between stochastic regular grammars. Theoretical Informatics and Applications. To appear.Google Scholar
  6. Carrasco, R.C. & Oncina, J. (1994): Learning stochastic regular grammars by means of a state merging method in “Grammatical Inference and Applications” (R.C. Carrasco and J. Oncina, Eds.). Lecture Notes in Artificial Intelligence 862, Springer-Verlag, Berlin.Google Scholar
  7. Cover, T.M. & Thomas, J.A. (1991): Elements of Information Theory. John Wiley and Sons, New York.Google Scholar
  8. Hoeffding, W. (1963): Probability inequalities for sums of bounded random variables. American Statistical Association Journal 58, 13–30.zbMATHMathSciNetCrossRefGoogle Scholar
  9. Hopcroft, J.E. & Ullman, J.D. (1979): “Introduction to automata theory, languages and computation”. Addison Wesley, Reading, Massachusetts.Google Scholar
  10. Oncina, J. &. García, P. (1994): Inference of rational tree sets. Universidad Politécnica de Valencia, Internal Report DSIC-ii-1994-23.Google Scholar
  11. Sakakibara, Y. (1992): Efficient learning of context-free grammars from positive structural examples. Information and Computation 97, 23–60.zbMATHMathSciNetCrossRefGoogle Scholar
  12. Stolcke, A. & Omohundro, S. (1993): Hidden Markov model induction by Bayesian model merging in “Advances in Neural Information Processing Systems 5” (C.L. Giles, S.J. Hanson and J.D. Cowan, Eds.). Morgan-Kaufman, Menlo Park, California.Google Scholar
  13. Wetherell, C.S. (1980): Probabilistic Languages: A Review and Some Open Questions ACM Computing Survey 12 361–379zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Rafael C. Carrasco
    • 1
  • Jose Oncina
    • 1
  • Jorge Calera
    • 1
  1. 1.Departamento de Lenguajes y Sistemas InformáticosUniversidad de AlicanteAlicante

Personalised recommendations