Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs

  • Farid Ablayev
  • Aida Gainutdinova
  • Kamil Khadiev
  • Abuzer Yakaryılmaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8614)


In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models.
  • We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1.

  • We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient than classical nondeterminism. In particular, an explicit function is presented which is computed by a quantum nondeterministic OBDD with constant width, but any classical nondeterministic OBDD for this function needs non-constant width.

  • We also present new hierarchies on widths of deterministic and nondeterministic OBDDs. We focus both on small and large widths.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ablayev, F.: Randomization and nondeterminsm are incomparable for ordered read-once branching programs. Electronic Colloquium on Computational Complexity (ECCC) 4(21) (1997)Google Scholar
  2. 2.
    Ablayev, F., Gainutdinova, A.: Complexity of quantum uniform and nonuniform automata. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 78–87. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Ablayev, F., Gainutdinova, A., Karpinski, M.: On computational power of quantum branching programs. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 59–70. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Ablayev, F., Gainutdinova, A., Khadiev, K., Yakaryılmaz, A.: Very narrow quantum OBDDs and width hierarchies for classical OBDDs. Technical Report arXiv:1405.7849, arXiv (2014)Google Scholar
  5. 5.
    Ablayev, F.M., Gainutdinova, A., Karpinski, M., Moore, C., Pollett, C.: On the computational power of probabilistic and quantum branching program. Information Computation 203(2), 145–162 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Ablayev, F.M., Karpinski, M.: On the power of randomized branching programs. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 348–356. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  7. 7.
    Ambainis, A., Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In: FOCS, pp. 332–341. IEEE Computer Society (1998),
  8. 8.
    Ambainis, A., Yakaryılmaz, A.: Superiority of exact quantum automata for promise problems. Information Processing Letters 112(7), 289–291 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Bertoni, A., Carpentieri, M.: Analogies and differences between quantum and stochastic automata. Theoretical Computer Science 262(1-2), 69–81 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Geffert, V., Yakaryılmaz, A.: Classical automata on promise problems. In: DCFS 2014. LNCS, vol. 8614, pp. 125–136. Springer, Heidelberg (2014)Google Scholar
  11. 11.
    Hromkovič, J., Sauerhoff, M.: Tradeoffs between nondeterminism and complexity for communication protocols and branching programs. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 145–156. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Hromkovic, J., Sauerhoff, M.: The power of nondeterminism and randomness for oblivious branching programs. Theory of Computing Systems 36(2), 159–182 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: FOCS, pp. 66–75. IEEE Computer Society (1997)Google Scholar
  14. 14.
    Nakanishi, M., Hamaguchi, K., Kashiwabara, T.: Ordered quantum branching programs are more powerful than ordered probabilistic branching programs under a bounded-width restriction. In: Du, D.-Z., Eades, P., Sharma, A.K., Lin, X., Estivill-Castro, V. (eds.) COCOON 2000. LNCS, vol. 1858, pp. 467–476. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Paz, A.: Introduction to Probabilistic Automata. Academic Press, New York (1971)zbMATHGoogle Scholar
  16. 16.
    Rashid, J., Yakaryılmaz, A.: Implications of quantum automata for contextuality. In: Holzer, M., Kutrib, M. (eds.) CIAA 2014. LNCS, vol. 8587, pp. 318–331. Springer, Heidelberg (2014)Google Scholar
  17. 17.
    Sauerhoff, M., Sieling, D.: Quantum branching programs and space-bounded nonuniform quantum complexity. Theoretical Computer Science 334(1-3), 177–225 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Watrous, J.: On the complexity of simulating space-bounded quantum computations. Computational Complexity 12(1-2), 48–84 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Watrous, J.: Quantum computational complexity. In: Encyclopedia of Complexity and System Science. Springer arXiv:0804.3401 (2009)Google Scholar
  20. 20.
    Wegener, I.: Branching Programs and Binary Decision Diagrams. SIAM (2000)Google Scholar
  21. 21.
    Yakaryılmaz, A., Say, A.C.C.: Languages recognized by nondeterministic quantum finite automata. Quantum Information and Computation 10(9-10), 747–770 (2010)zbMATHMathSciNetGoogle Scholar
  22. 22.
    Yakaryılmaz, A., Say, A.C.C.: Unbounded-error quantum computation with small space bounds. Information and Computation 279(6), 873–892 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Farid Ablayev
    • 1
  • Aida Gainutdinova
    • 1
  • Kamil Khadiev
    • 1
  • Abuzer Yakaryılmaz
    • 2
    • 3
  1. 1.Kazan Federal UniversityKazanRussia
  2. 2.Faculty of ComputingUniversity of LatviaRigaLatvia
  3. 3.National Laboratory for Scientific ComputingPetrópolisBrazil

Personalised recommendations