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The Theory of Zero-Suppressed BDDs and the Number of Knight's Tours

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Abstract

Zero-suppressed binary decision diagrams (ZBDDs) have been introduced by Minato [14–17] who presents applications for cube set representations, fault simulation, timing analysis and the n-queens problem. Here the structural properties of ZBDDs are worked out and a generic synthesis algorithm is presented and analyzed. It is proved that ZBDDs can be at most by a factor n + 1 smaller or larger than ordered BDDs (OBDDs) for the same function on n variables. Using ZBDDs the best known upper bound on the number of knight's tours on an 8 × 8 chessboard is improved significantly.

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Authors and Affiliations

  1. FB Informatik, LS II, Univ. Dortmund, 44221, Dortmund, Germany

    Olaf Schröer & Ingo Wegener

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  1. Olaf Schröer
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  2. Ingo Wegener
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Schröer, O., Wegener, I. The Theory of Zero-Suppressed BDDs and the Number of Knight's Tours. Formal Methods in System Design 13, 235–253 (1998). https://doi.org/10.1023/A:1008681625346

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  • DOI: https://doi.org/10.1023/A:1008681625346

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