Abstract
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 2k + 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ablayev, F.: Randomization and nondeterminsm are incomparable for ordered read-once branching programs. Electronic Colloquium on Computational Complexity (ECCC) 4(21) (1997)
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)
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)
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)
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)
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)
Ambainis, A., Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In: FOCS, pp. 332–341. IEEE Computer Society (1998), http://arxiv.org/abs/quant-ph/9802062
Ambainis, A., Yakaryılmaz, A.: Superiority of exact quantum automata for promise problems. Information Processing Letters 112(7), 289–291 (2012)
Bertoni, A., Carpentieri, M.: Analogies and differences between quantum and stochastic automata. Theoretical Computer Science 262(1-2), 69–81 (2001)
Geffert, V., Yakaryılmaz, A.: Classical automata on promise problems. In: DCFS 2014. LNCS, vol. 8614, pp. 125–136. Springer, Heidelberg (2014)
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)
Hromkovic, J., Sauerhoff, M.: The power of nondeterminism and randomness for oblivious branching programs. Theory of Computing Systems 36(2), 159–182 (2003)
Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: FOCS, pp. 66–75. IEEE Computer Society (1997)
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)
Paz, A.: Introduction to Probabilistic Automata. Academic Press, New York (1971)
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)
Sauerhoff, M., Sieling, D.: Quantum branching programs and space-bounded nonuniform quantum complexity. Theoretical Computer Science 334(1-3), 177–225 (2005)
Watrous, J.: On the complexity of simulating space-bounded quantum computations. Computational Complexity 12(1-2), 48–84 (2003)
Watrous, J.: Quantum computational complexity. In: Encyclopedia of Complexity and System Science. Springer arXiv:0804.3401 (2009)
Wegener, I.: Branching Programs and Binary Decision Diagrams. SIAM (2000)
Yakaryılmaz, A., Say, A.C.C.: Languages recognized by nondeterministic quantum finite automata. Quantum Information and Computation 10(9-10), 747–770 (2010)
Yakaryılmaz, A., Say, A.C.C.: Unbounded-error quantum computation with small space bounds. Information and Computation 279(6), 873–892 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ablayev, F., Gainutdinova, A., Khadiev, K., Yakaryılmaz, A. (2014). Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-09704-6_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09703-9
Online ISBN: 978-3-319-09704-6
eBook Packages: Computer ScienceComputer Science (R0)