Abstract.
Free binary decision diagrams (FBDDs) are graph-based data structures representing Boolean functions with the constraint (additional to binary decision diagram) that each variable is tested at most once during the computation. The function EAR n is the following Boolean function defined for n × n Boolean matrices: EAR n (M) = 1 iff the matrix M contains two equal adjacent rows. We prove that each FBDD computing EAR n has size at least \( 2^{{0.63\log ^{2}_{2} n - O(\log n\log \log n)}} \) and we present a construction of such diagrams of size approximately \( 2^{{1.89\log ^{2}_{2} n + O(\log n)}} \).
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Kára, J., Král’, D. Free binary decision diagrams for the computation of EAR n . comput. complex. 15, 40–61 (2006). https://doi.org/10.1007/s00037-006-0206-5
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DOI: https://doi.org/10.1007/s00037-006-0206-5