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.
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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.
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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.
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We also present new hierarchies on widths of deterministic and nondeterministic OBDDs. We focus both on small and large widths.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-319-09704-6_6
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