INTERPOLATING ARITHMETIC READ-ONCE FORMULAS IN PARALLEL

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dc.contributor.authorBshouty, Nader H.eng
dc.contributor.authorCleve, Richardeng
dc.date.accessioned2008-02-27T16:49:46Z
dc.date.available2008-02-27T16:49:46Z
dc.date.computerscience1999-05-27eng
dc.date.issued1995-05-01eng
dc.description.abstractA formula is read-once if each variable appears at most once in it. An artithmetic read-once formula is one in which the operations are addition, subtraction, multiplication, and division (and constants are allowed). We present a randomized (Las Vegas) parallel algorithm for the exact interpolation of arithmetic read-once formulas over sufficiently large fields. More specifically, for n-variable read-once formulas, and fields of size at least $3(n sup 2 + 3n - 2)$, our algorithm runs in $O(log sup 2 n)$ parallel steps using $O(n sup 4)$ processors (where the field operations are charged unit cost). This complements other results which imply that other classes of read-once formulas cannot be interpolated-or even learned with membership and equivalence queries-in poly-logarithmic-time with polynomially many processors (even though they can be learned sequentially in polynomial-time). These classes include boolean read-once formulas and arithmetic read-once formulas over fields of size o(n/log n) (for n variable read-once formulas).eng
dc.description.notesWe are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.caeng
dc.identifier.department1995-569-21eng
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/30478
dc.identifier.urihttp://hdl.handle.net/1880/45752
dc.language.isoEngeng
dc.publisher.corporateUniversity of Calgaryeng
dc.publisher.facultyScienceeng
dc.subjectComputer Scienceeng
dc.titleINTERPOLATING ARITHMETIC READ-ONCE FORMULAS IN PARALLELeng
dc.typeunknown
thesis.degree.disciplineComputer Scienceeng
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