%AGöös, Mika%AKamath, Pritish%ASotiraki, Katerina%AZampetakis, Manolis%Anull Ed.%D2020%I
%K
%MOSTI ID: 10220397
%PMedium: X
%TOn the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem
%XWe study the search problem class PPA_q defined as a modulo-q analog of the well-known polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA_p for prime p. Our main result is to establish that an explicit version of a search problem associated to the Chevalley - Warning theorem is complete for PPA_p for prime p. This problem is natural in that it does not explicitly involve circuits as part of the input. It is the first such complete problem for PPA_p when p ≥ 3. Finally we discuss connections between Chevalley-Warning theorem and the well-studied short integer solution problem and survey the structural properties of PPA_q.
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