Extremal bipartite graphs and superpolynomial lower bounds for monotone span programs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
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Span programs provide a linear algebraic model of computation. Lower Bounds for span programs imply lower bounds for formula size, symmetric branching programs and for contact schemes. Monotone span programs correspond also to linear secret-sharing schemes. We present a new technique for proving lower bounds for monotone span programs, and prove a lower bound of /spl Omega/(m/sup 2.5/) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.