Lower bounds for monotone span programs

Amos Beimel, Mike Paterson, Anna Gál

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

Span programs provide a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for formula size, symmetric branching programs, and 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. We prove a lower bound of Ω(m2.5) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.

Original languageEnglish
Pages (from-to)29-45
Number of pages17
JournalComputational Complexity
Volume6
Issue number1
DOIs
StatePublished - 1 Jan 1996
Externally publishedYes

Keywords

  • Lower bounds
  • Monotone complexity classes
  • Secret sharing
  • Span programs

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