Probabilistic algorithms

  • Authors:

  • Azaria Paz

  • Affiliations:

  • -

  • Venue:
  • Encyclopedia of Computer Science
  • Year:
  • 2003

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Abstract

Let Q(x, y) be the two-variable polynomial Q(x, y) = (x + y)7 - x7 - y7 - 7xy(x + y)(x2 + xy + y2)2 and assume that we want to ascertain whether Q(x, y) is identically equal to zero. A deterministic algorithm for this task would be to expand Q(x, y) to individual terms, opening all parentheses, and then cancel out all equal terms with opppsite signs. Q(x, y) is identically zero if and only if all the terms cancel. A probabilistic algorithm for the same problem can be described as follows: