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This paper gives nearly optimal lower bounds on the minimum degree of polynomial calculus refutations of Tseitin's graph tautologies and the mod p counting principles, p 2. The lower bounds apply to the polynomial calculus over elds or rings. These are the rst linear lower bounds for polynomial calculus; moreover, they distinguish linearly between proofs(More)
The authors consider the problem of reconstructing (i.e., interpolating) a t-sparse multivariate polynomial given a black box which will produce the value of the polynomial for any value of the arguments. It is shown that, if the polynomial has coefficients in a finite field GF[q] and the black box can evaluate the polynomial in the field GF[qr2g,tnt+37],(More)