computational complexity

, Volume 6, Issue 1, pp 29–45

Lower bounds for monotone span programs

  • Amos Beimel
  • Anna Gál
  • Mike Paterson

DOI: 10.1007/BF01202040

Cite this article as:
Beimel, A., Gál, A. & Paterson, M. Comput Complexity (1996) 6: 29. doi:10.1007/BF01202040


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.

Key words

Span programssecret sharingmonotone complexity classeslower bounds

Subject classifications


Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Amos Beimel
    • 1
  • Anna Gál
    • 3
  • Mike Paterson
    • 2
  1. 1.Department of Computer Science TechnionHaifaIsrael
  2. 2.Department of Computer ScienceUniversity of WarwickCoventryUK
  3. 3.School of MathematicsInstitute for Advanced StudyPrincetonUSA