On arithmetic branching programs

A. Beimel, A. Gál

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


We consider the model of arithmetic branching programs, which is a generalization of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs. Using this equivalence we prove that dependency programs are closed under conjunction over every field. Furthermore, we show that span programs, an algebraic model of computation introduced by M. Karchmer and A. Wigderson (1993), are at least as strong as arithmetic programs; every arithmetic program can be simulated by a span program of size nod more than twice the size of the arithmetic program. Using the above results we give a new proof that NL/poly ⊆ ⊕ L/poly, first proved by A. Wigderson (1995). Our simulation of NL/poly is more efficient, and it holds for logspace counting classes over every field.

Original languageEnglish
Title of host publicationProceedings - 13th Annual IEEE Conference on Computational Complexity, CCC 1998
PublisherInstitute of Electrical and Electronics Engineers
Number of pages13
ISBN (Print)0818683953
StatePublished - 1 Jan 1998
Externally publishedYes
Event13th Annual IEEE Conference on Computational Complexity, CCC 1998 - Buffalo, United States
Duration: 15 Jun 199818 Jun 1998

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159


Conference13th Annual IEEE Conference on Computational Complexity, CCC 1998
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics


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