Some Exact Complexity Results for Straight-Line Computations over Semirings

Mark Jerrum, Marc Snir

Research output: Contribution to journalArticlepeer-review


The problem of computing polynomials in certain semmngs is considered. Precise bounds are obtained on the number of multiplications required by straight-hne algorithms which compute such functions as iterated matrix multiplication, iterated convolution, and permanent Usmg these bounds, tt is shown that the use of branching can exponentially speed up computations using the min, + operations, and that subtraction can exponentially speed up arithmetic computations These results can be interpreted as denying the existence of fast “universal” algorithms for computing certain polynomials.

Original languageEnglish (US)
Pages (from-to)874-897
Number of pages24
JournalJournal of the ACM (JACM)
Issue number3
StatePublished - Jul 1 1982
Externally publishedYes


  • Farkas Lemma
  • artthmeuc complexity
  • convexity theory
  • minimax algebra
  • straight-hne algorithm

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Hardware and Architecture
  • Artificial Intelligence


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