Reconstructing Algebraic Functions from Mixed Data

We consider a variant of the traditional task of explicitly reconstructing algebraic functions from black box representations. In the traditional setting for such problems, one is given access to an unknown function f that is represented by a black box, or an oracle, which can be queried for the value of f at any input. Given a guarantee that this unknown function f is some nice algebraic function, say a polynomial in its input of degree bound d, the goal of the reconstruction problem is to explicitly determine the coefficients of the unknown polynomial. All work on polynomial interpolation, especially sparse ones, are or may be presented in such a setting. The work of Kaltofen and Trager [25], for instance, highlights the utility of this setting, by performing numerous manipulations on polynomials presented as black boxes. The variant considered in this paper differs from the traditional setting in that our black boxes represent several algebraic functions

• Type: Conference
• Year: 1992
• Where: FOCS
• Authors: Sigal Ar, Richard J. Lipton, Ronitt Rubinfeld, Madhu Sudan
• Keywords: Algebraic Function, Black Box, FOCS 1992, Polynomial, Theoretical Computer Science