Combinatorial characterization of read-once formulae
Discrete Mathematics - Special issue on combinatorics and algorithms
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
Lower bounds for monotone span programs
Computational Complexity
Communication complexity
A characterization of span program size and improved lower bounds for monotone span programs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
On notions of information transfer in VLSI circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On Linear Secret Sharing for Connectivity in Directed Graphs
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Secret-sharing schemes: a survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
On the size of monotone span programs
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
On the incompressibility of monotone DNFs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We shall give simpler proofs of some lower bounds on monotone computations. We describe a simple condition on combinatorial structures, such that the rank of the matrix associated with these structures gives lower bounds on monotone span program size and monotone formula size. We also prove an upper bound on the rank of the corresponding matrices, and show that such structures can be constructed from self-avoiding families. As a corollary, we obtain an upper bound on the size of self-avoiding families, which solves a problem posed by Babai and Gál [Combinatorica 19 (3) (1999) 301-319].