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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)

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 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.

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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

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