Free binary decision diagrams for the computation of EAR _n

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 $2^{{1.89\log ^{2}_{2} n + O(\log n)}}$.