Advertisement

Efficient learning of real time one-counter automata

  • Amr F. Fahmy
  • Robert S. Roos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 997)

Abstract

We present an efficient learning algorithm for languages accepted by deterministic real time one-counter automata (ROCA). The learning algorithm works by first learning an initial segment, B n , of the infinite state machine that accepts the unknown language and then decomposing it into a complete control structure and a partial counter. A new, efficient ROCA decomposition algorithm, which will be presented in detail, allows this result. The decomposition algorithm works in time O(n2log(n)) where nc is the number of states of B n for some language-dependent constant c. If Angluin's algorithm for learning regular languages is used to learn B n and the complexity of this step is h(n, m), where m is the length of the longest counterexample necessary for Angluin's algorithm, the complexity of our algorithm is O(h(n,m) + n2log(n)).

Keywords

State Machine Finite State Machine Regular Language Exit Point Input String 
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.

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 counter examples. Information and Computation 75 (1987) 87–106CrossRefGoogle Scholar
  2. 2.
    Berman, P., Roos, R.: Learning one-counter languages in polynomial time. Proceedings of the 28th IEEE Symposium on Foundations of Computer Science (1987) 61–67Google Scholar
  3. 3.
    Biermann, A.W.: A fundamental theorem for real time programs. Duke Univerity Department of Computer Science technical report (1977)Google Scholar
  4. 4.
    Fahmy, A. F., Biermann, A. W.: Synthesis of real time acceptors. Journal of Symbolic Computation 15 (1993) 807–842Google Scholar
  5. 5.
    Fahmy, A. F.: Synthesis of Real Time Programs. PhD thesis, Duke University, 1989Google Scholar
  6. 6.
    Hartmanis, J., Stearns, R.E.: Algebraic Structure Theory of Sequential Machines. (1966: Prentice-Hall)Google Scholar
  7. 7.
    Main, M., Lorentz, R.: An O(n log(n)) algorithm for finding all repetitions in a string. Journal of Algorithms 5 (1984) 422–432CrossRefGoogle Scholar
  8. 8.
    Roos, R.: Deciding Equivalence of Deterministic One-Counter Automata in Polynomial Time with Applications to Learning. PhD thesis, The Pennsylvania State University, 1988Google Scholar
  9. 9.
    Valiant, L. G., Paterson, M. S.: Deterministic one-counter automata. Journal of Computer and System Sciences 10 (1975) 340–350Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Amr F. Fahmy
    • 1
  • Robert S. Roos
    • 2
  1. 1.Aiken Computation LabHarvard UniversityCambridgeUSA
  2. 2.Department of Computer ScienceSmith CollegeNorthamptonUSA

Personalised recommendations