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Error-Free Affine, Unitary, and Probabilistic OBDDs

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Descriptional Complexity of Formal Systems (DCFS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10952))

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Abstract

We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata versions of these models.

Part of the research work was done while Ibrahimov was visiting University of Latvia in February 2017.

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Notes

  1. 1.

    It evolves linearly but a non-linear operator is applied when we retrieve information from the state vector.

  2. 2.

    Suppose we have \(w_i\le m\) nodes on a level i; then the node \(u_j\) of this level corresponds to the state \(s_j\), for \(j\in \{1,\dots ,w_i\}\).

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Acknowledgements

We thank Evgenijs Vihrovs (University of Latvia) for his helpful discussions and anonymous reviewers for their very helpful comments.

The work is partially supported by ERC Advanced Grant MQC, Latvian State Research Programme NeXIT project No. 1. The work is also performed according to the Russian Government Program of Competitive Growth of Kazan Federal University. The research on Las-Vegas OBDDs (Sect. 5) is supported by Russian Science Foundation Grant 17-71-10152

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Authors and Affiliations

  1. Kazan Federal University, Kazan, Russia

    Rishat Ibrahimov & Kamil Khadiev

  2. Center for Quantum Computer Science, University of Latvia, Rīga, Latvia

    Kamil Khadiev, Krišjānis Prūsis & Abuzer Yakaryılmaz

  3. Smart Quantum Technologies Ltd., Kazan, Russia

    Rishat Ibrahimov & Kamil Khadiev

Authors
  1. Rishat Ibrahimov
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  2. Kamil Khadiev
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  3. Krišjānis Prūsis
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  4. Abuzer Yakaryılmaz
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Correspondence to Kamil Khadiev .

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Editors and Affiliations

  1. Department of Mathematics and Computing Science, Saint Mary’s University, Halifax, Nova Scotia, Canada

    Stavros Konstantinidis

  2. Dipartimento di Informatica e Comunicazi, Universita degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

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Ibrahimov, R., Khadiev, K., Prūsis, K., Yakaryılmaz, A. (2018). Error-Free Affine, Unitary, and Probabilistic OBDDs. In: Konstantinidis, S., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2018. Lecture Notes in Computer Science(), vol 10952. Springer, Cham. https://doi.org/10.1007/978-3-319-94631-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-94631-3_15

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