In 1993 Karchmer and Wigderson introduced an interesting linear algebraic model for computing boolean functions—the span program. A span program is just a matrix over some field with rows labeled by literals. (In this chapter we will only work over the field GF(2), but the results hold for any field.) The span program accepts an input assignment if and only if the all-1 vector can be obtained as a linear combination of the rows whose labels are satisfied by the input. The size of the span program is the number of rows in the matrix. A span program is monotone if only positive literals are used as labels of the rows, that is, negated variables are not allowed.
KeywordsBipartite Graph Boolean Function Nonzero Entry Secret Sharing Scheme Positive Literal
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