Advertisement

On the Hierarchy Classes of Finite Ultrametric Automata

  • Rihards Krišlauks
  • Kaspars Balodis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8939)

Abstract

This paper explores the language classes that arise with respect to the head count of a finite ultrametric automaton. First we prove that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognized by any k-head non-deterministic finite automaton. Then we prove that in the two-way setting the class of languages recognized by ultrametric finite k-head automata is a proper subclass of the class of languages recognized by (k + 1)-head automata. Ultrametric finite automata are similar to probabilistic and quantum automata and have only just recently been introduced by Freivalds. We introduce ultrametric Turing machines and ultrametric multi-register machines to assist in proving the results.

Keywords

Turing Machine Ultrametric Analysis Hierarchy Class Language Class Input Word 
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.
    Balodis, K., Beriņa, A., Cīpola, K., Dimitrijevs, M., Iraids, J., Jēriņš, K., Kacs, V., Kalējs, J., Krišlauks, R., Lukstiņš, K., Raumanis, R., Scegulnaja, I., Somova, N., Vanaga, A., Freivalds, R.: On the state complexity of ultrametric finite automata. In: SOFSEM 2013: Theory and Practice of Computer Science. vol. 2, pp. 1–9 (2013)Google Scholar
  2. 2.
    Dragovich, B., Dragovich, A.: A p-adic model of DNA sequence and genetic code. p-Adic Numbers, Ultrametric Analysis, and Applications 1(1), 34–41 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Freivalds, R.: Ultrametric automata and Turing machines. In: Voronkov, A. (ed.) Turing-100. EPiC Series, vol. 10, pp. 98–112. EasyChair (2012)Google Scholar
  4. 4.
    Freivalds, R.: Language recognition using finite probabilistic multitape and multihead automata. Problemy Peredachi Informatsii 15(3), 99–106 (1979) (in Russian)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Holzer, M., Kutrib, M., Malcher, A.: Multi-head finite automata: Characterizations, concepts and open problems. Electronic Proceedings in Theoretical Computer Science 1, 93–107 (2009), http://dx.doi.org/10.4204/EPTCS.1.9 CrossRefGoogle Scholar
  6. 6.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley (1979)Google Scholar
  7. 7.
    Kozyrev, S.V.: Ultrametric analysis and interbasin kinetics, pp. 121–128. American Institute of Physics (2006)Google Scholar
  8. 8.
    Krišlauks, R., Rukšāne, I., Balodis, K., Kucevalovs, I., Freivalds, R., Nāgele, I.: Ultrametric Turing machines with limited reversal complexity. In: SOFSEM 2013: Theory and Practice of Computer Science. vol. 2, pp. 87–94 (2013)Google Scholar
  9. 9.
    Macarie, I.: Multihead two-way probabilistic finite automata. In: Baeza-Yates, R., Poblete, P.V., Goles, E. (eds.) LATIN 1995. LNCS, vol. 911, pp. 371–385. Springer, Heidelberg (1995), http://dx.doi.org/10.1007/3-540-59175-3_103 CrossRefGoogle Scholar
  10. 10.
    Madore, D.A.: A first introduction to p-adic numbers. Online (2000), http://www.madore.org/~david/math/padics.eps
  11. 11.
    Monien, B.: Two-way multihead automata over a one-letter alphabet. RAIRO - Theoretical Informatics and Applications - Informatique Thorique et Applications 14(1), 67–82 (1980)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Turakainen, P.: Generalized automata and stochastic languages. Proceedings of The American Mathematical Society 21, 303–309 (1969)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Yao, A.C., Rivest, R.L.: k + 1 heads are better than k. vol. 25, pp. 337–340. ACM, New York (1978), http://doi.acm.org/10.1145/322063.322076

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Rihards Krišlauks
    • 1
  • Kaspars Balodis
    • 1
  1. 1.University of Latvia Faculty of ComputingRigaLatvia

Personalised recommendations