Lower Bounds for Polynomial Calculus: Non-Binomial Case

Authors:
M. Alekhnovich;A. Razborov
Affiliations:
-;-
Venue:
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Year:
2001

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Abstract

We generalize recent linear lower bounds for Polynomial Calculus based on binomial ideals. We produce a general hardness criterion (that we call immunity) which is satisfied by a random function and prove linear lower bounds on the degree of PC refutations for a wide class of tautologies based on immune functions. As some applications of our techniques, we introducemodp Tseitin tautologies in the Boolean case (e.g. in the presence of axioms x_i^2= x_i), prove that they are hard for PC over fields with characteristic different from p, and generalize them to Flow tautologies which are based on the MAJORITY function and are proved to be hard over any field. We also show the \Omega (n) lower bound for random k-CNF's over fields of characteristic 2.