Real-Time Vector Automata

  • Özlem Salehi
  • Abuzer Yakaryılmaz
  • A. C. Cem Say
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8070)


We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected k×k matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and “blind” versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.


vector automata counter automata automata with multiplication generalized automata 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Counter machines and counter languages. Mathematical Systems Theory 2(3), 265–283 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Greibach, S.A.: Remarks on blind and partially blind one-way multicounter machines. Theoretical Computer Science 7, 311–324 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Ibarra, O.H., Sahni, S.K., Kim, C.E.: Finite automata with multiplication. Theoretical Computer Science 2(3), 271 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Turakainen, P.: Generalized automata and stochastic languages. Proceedings of the American Mathematical Society 21, 303–309 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Yakaryılmaz, A.: Superiority of one-way and realtime quantum machines. RAIRO - Theoretical Informatics and Applications 46(4), 615–641 (2012)zbMATHCrossRefGoogle Scholar
  6. 6.
    Laing, R.: Realization and complexity of commutative events. Technical report, University of Michigan (1967)Google Scholar
  7. 7.
    Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Real time counter machines. In: Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967). FOCS 1967, pp. 148–154. IEEE Computer Society, Washington, DC (1967)Google Scholar
  8. 8.
    Diêu, P.D.: Criteria of representability of languages in probabilistic automata. Cybernetics and Systems Analysis 13(3), 352–364 (1977); Translated from Kibernetika (3), 39–50, (May-June 1977)Google Scholar
  9. 9.
    Freivalds, R.: Probabilistic two-way machines. In: Proceedings of the International Symposium on Mathematical Foundations of Computer Science, pp. 33–45 (1981)Google Scholar
  10. 10.
    Dwork, C., Stockmeyer, L.: Finite state verifiers I: The power of interaction. Journal of the ACM 39(4), 800–828 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Ravikumar, B.: Some observations on 2-way probabilistic finite automata. In: Shyamasundar, R.K. (ed.) FSTTCS 1992. LNCS, vol. 652, pp. 392–403. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  12. 12.
    Diêu, P.D.: On a class of stochastic languages. Mathematical Logic Quarterly 17(1), 421–425 (1971)zbMATHCrossRefGoogle Scholar
  13. 13.
    Yakaryilmaz, A.: Quantum Alternation. In: Bulatov, A.A., Shur, A.M. (eds.) CSR 2013. LNCS, vol. 7913, pp. 334–346. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Özlem Salehi
    • 1
    • 2
  • Abuzer Yakaryılmaz
    • 3
  • A. C. Cem Say
    • 1
  1. 1.Department of Computer EngineeringBoǧaziçi UniversityBebekTurkey
  2. 2.Department of MathematicsBoǧaziçi UniversityBebekTurkey
  3. 3.Faculty of ComputingUniversity of LatviaRīgaLatvia

Personalised recommendations