Acta Informatica

, Volume 48, Issue 1, pp 43–50

New bounds for the query complexity of an algorithm that learns DFAs with correction and equivalence queries

Original Article
  • 38 Downloads

Abstract

In this note, we show that the number of equivalence queries asked by an algorithm proposed in Becerra-Bonache et al. (Proceedings of the 8th International Colloquium on Grammatical Inference (ICGI ’06), Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin 2006) that learns deterministic finite automata with correction and equivalence queries is at most the injectivity degree of the target language, a notion that corresponds to the number of repetitions among the correcting words of all the elements in the quotient of that language by the Myhill-Nerode equivalence. Further, we propose a tight upper bound for the number of correction queries as a function which depends on the index of the target language, the length of the longest counterexample returned by the teacher and the injectivity degree of the target language. However, the bounds obtained here for the number of CQs are optimal for the LCA algorithm, and they do not represent a tight upper bound for DFA learning with EQs and CQs in general.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Angluin D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Becerra-Bonache L., Dediu A.H., Tîrnăucă C.: Learning DFA from correction and equivalence queries. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds) Proceedings of the 8th International Colloquium on Grammatical Inference (ICGI’06), Lecture Notes in Artificial Intelligence, vol. 4201, pp. 281–292. Springer-Verlag, Berlin, Heidelberg (2006)Google Scholar
  3. 3.
    Martín-Vide, C., Mitrana, V., Păun, G. (eds): Formal Languages and Applications. Studies in Fuzzyness and Soft Computing, vol. 148. Springer-Verlag, Heidelberg, Berlin (2004)Google Scholar
  4. 4.
    Myhill, J.: Finite automata and the representation of events. Technical Report. TR-57-624,WADD, Wright Patterson AFB, Ohio (1957)Google Scholar
  5. 5.
    Nerode, A.: Linear automaton transformations. In: Proceedings of the American Mathematical Society, vol. 9, 541–544 (1958)Google Scholar
  6. 6.
    Rivest R.L., Schapire R.E.: Inference of finite automata using homing sequences. Inf. Comput. 103(2), 299–347 (1993)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Tîrnăucă, C.: Language learning with correction queries. Ph.D. Thesis, University of Tarragona (2009). http://www.tdr.cesca.es/TESIS_URV/AVAILABLE/TDX-0302109-134530/Thesis.pdf

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Depto. Organización y Estructura de la InformaciónUniversidad Politécnica de MadridMadridSpain
  2. 2.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

Personalised recommendations