Span Programs

Chapter
Part of the Algorithms and Combinatorics book series (AC, volume 27)

Abstract

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.

Keywords

Bipartite Graph Boolean Function Nonzero Entry Secret Sharing Scheme Positive Literal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of FrankfurtFrankfurt am MainGermany
  2. 2.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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