Very narrow quantum OBDDs and width hierarchies for classical OBDDs
- Authors: Ablayev F.1, Gainutdinova A.1, Khadiev K.1, Yakaryılmaz A.2
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Affiliations:
- Department of Theoretical Cybernetics, Institute of Computational Mathematics and Information Technologies
- Hurriyet Mah. 1755. Sok. 8/5, Yenisehir
- Issue: Vol 37, No 6 (2016)
- Pages: 670-682
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198367
- DOI: https://doi.org/10.1134/S199508021606007X
- ID: 198367
Cite item
Abstract
In the paper we investigate Ordered Binary Decision Diagrams (OBDDs)–a model for computing Boolean functions. We present a series of results on the comparative complexity for several variants of OBDDmodels.
• We present 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 nondeterminismcan bemore efficient than classical nondeterminism. In particular, an explicit function is presented that is computed by a quantum nondeterministic OBDD of 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.
About the authors
F. Ablayev
Department of Theoretical Cybernetics, Institute of Computational Mathematics and Information Technologies
Author for correspondence.
Email: fablayev@gmail.com
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatrstan, 420008
A. Gainutdinova
Department of Theoretical Cybernetics, Institute of Computational Mathematics and Information Technologies
Email: fablayev@gmail.com
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatrstan, 420008
K. Khadiev
Department of Theoretical Cybernetics, Institute of Computational Mathematics and Information Technologies
Email: fablayev@gmail.com
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatrstan, 420008
A. Yakaryılmaz
Hurriyet Mah. 1755. Sok. 8/5, Yenisehir
Email: fablayev@gmail.com
Turkey, Mersin, 33120