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Title: On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem
We 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.  more » « less
Award ID(s):
1741137
NSF-PAR ID:
10220397
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Computational Complexity Conference 2020
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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