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CSReports 19851989  Copyright 19851989 University of Bonn, Department of Computer Science, Abt. V  
8522 01.12.2008 
On ZeroTesting and Interpolation of kSparse Multivariate Polynomials over Finite Fields
Michael Clausen, Andreas Dress, Johannes Grabmeier and Marek Karpinski [Download PostScript] [Download PDF] Given a black box which will produce the value of a ksparse multivariate polynomial for any given specific argument, one may ask for optimal strategies (1) to distinguish such a polynomial from the zero polynomial, (2) to distinguish any two such polynomials from each other and (3) to (uniformly) reconstruct the polynomial from such an information source. While such strategies are known already for polynomials over fields of characteristic zero, the equally important, but considerably more complicated case of a finite filed K is studied in the present paper. The result is that the time complexity of such strategies depends critically on the degree of m of the extension filed of K from which the arguments are to be chosen; e.g. if m equals the number n of variables, then (1) can be solved by k + 1 and (2) as well as (3) by 2k + 1 queries, while in case m = 1 essentially 2^{log n log k} queries are needed. 

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University of Bonn > Department of Computer Science > Chair V 