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On Unordered BDDs and Quantified Boolean Formulas

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Progress in Artificial Intelligence (EPIA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11805))

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Abstract

This paper proposes to study the synthesis of unordered binary decision diagrams (BDDs) using solvers for Quantified Boolean Formulas (QBF). The synthesis of a BDD falls naturally in the realm of quantified formulas as we are typically looking for a BDD satisfying a certain specification. This means that we ask whether there exists a BDD such that for all inputs the specification is satisfied. We show that this query can be encoded naturally into QBF and experimentally evaluate these queries for the minority function.

The short paper should be seen as a challenge for further research on QBF solving.

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Notes

  1. 1.

    For existing lower bounds for BDD see a survey by Razborov [14].

  2. 2.

    The majority function is obtained by swapping the semantics of 0 and 1, which is easy to do in BDDs.

  3. 3.

    Pudlák gives a \(\varOmega (n\lg n)\) lower-bound for this function [13].

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Acknowledgments

This work was supported by national funds through FCT - Fundação para a Ciência e a Tecnologia with reference UID/CEC/50021/2019 and the project INFOCOS with reference PTDC/CCI-COM/32378/2017.

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Authors and Affiliations

  1. IST/INESC-ID, Lisbon, Portugal

    Mikoláš Janota

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  1. Mikoláš Janota
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Correspondence to Mikoláš Janota .

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Editors and Affiliations

  1. INESC-TEC, University of Trás-os-Montes and Alto Douro, Vila Real, Portugal

    Paulo Moura Oliveira

  2. University of Minho, Braga, Portugal

    Paulo Novais

  3. LIACC/UP, University of Porto, Porto, Portugal

    Luís Paulo Reis

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Janota, M. (2019). On Unordered BDDs and Quantified Boolean Formulas. In: Moura Oliveira, P., Novais, P., Reis, L. (eds) Progress in Artificial Intelligence. EPIA 2019. Lecture Notes in Computer Science(), vol 11805. Springer, Cham. https://doi.org/10.1007/978-3-030-30244-3_41

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  • DOI: https://doi.org/10.1007/978-3-030-30244-3_41

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  • Print ISBN: 978-3-030-30243-6

  • Online ISBN: 978-3-030-30244-3

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