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A Deterministic Algorithm for Testing the Equivalence of Read-Once Branching Programs with Small Discrepancy

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Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

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Abstract

The problem to test the equivalence of two given read-once branching programs is a well-known problem in the class BPP that is not known to be solvable in deterministic polynomial time. The standard probabilistic algorithm to solve the problem reduces it to an instance of Polynomial Identity Testing and then applies the Schwartz-Zippel Lemma to test the equivalence. This method needs \(O(n\log n)\) random bits, where n is the number of variables in the branching programs. We provide a new method for testing the equivalence of read-once branching programs that uses \(O(\log n +\log |D|)\) random bits, where D is the set of assignments for which the two branching programs compute different results. This means O(n) random bits in the worst case and a deterministic polynomial time algorithm when the discrepancy set D is at most polynomial.

We also show that the equivalence test can be extended to the more powerful model of deterministic, decomposable negation normal forms (d-DNNFs).

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Authors and Affiliations

  1. Institute of Theoretical Computer Science, University of Ulm, Ulm, Germany

    Stefan Arnold & Jacobo Torán

Authors
  1. Stefan Arnold
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  2. Jacobo Torán
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Correspondence to Jacobo Torán .

Editor information

Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Åbo Akademi University, Turku, Finland

    Ion Petre

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Arnold, S., Torán, J. (2017). A Deterministic Algorithm for Testing the Equivalence of Read-Once Branching Programs with Small Discrepancy. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-58741-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

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