Linear Gaps Between Degrees for the Polynomial Calculus Modulo Distinct Primes (Abstract)

Two important algebraic proof systems are the Nullstellensatz system [1] and the polynomial calculus [2] (also called the Gröbner system). The Nullstellensatz system is a propositional proof system based on Hilbert’s Nullstellensatz, and the polynomial calculus (PC) is a proof system which allows derivations of polynomials, over some £eld. The complexity of a proof in these systems is measured in terms of the degree of the polynomials used in the proof. The mod p counting principle can be formulated as a set MOD p of constant-degree polynomials expressing the negation of the counting principle. The Tseitin mod p principles, TSn(p), are translations of the MOD n