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It is a known approach to translate propositional formulas into systems of polynomial inequalities and consider proof systems for the latter. The well-studied proof systems of this type are the Cutting Plane proof system (CP) utilizing linear inequalities and the Lovász– Schrijver calculi (LS) utilizing quadratic inequalities. We introduce generalizations(More)
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)
We introduce two versions of proof systems dealing with systems of inequalities: Positivstellensatz refutations and Positivstellensatz calculus. For both systems we prove the lower bounds on degrees and lengths of derivations for the example due to Lazard, Mora and Philip-pon. These bounds are sharp, as well as they are for the Nullstellen-satz refutations(More)
We analyse the computational complexity of sparse rational interpolation, and give the first deterministic algorithm for this problem with singly exponential bounds on the number of arithmetic operations. 1 A preliminary version of this paper has appeared in [10] 2 The first author would like to thank the Max Planck Institute in Bonn for its hospitality and(More)
It is established a lower bound on degrees of Positivstellensatz calculus refutations (over a real eld) introduced in GV 99], G 99], for the knapsack problem. The bound depends on the values of co-eecients of an instance of the knapsack problem: for certain values the lower bound is linear and for certain values the upper bound is constant, while in the(More)
We use the Litvinov-Maslov correspondence principle to reduce and hybridize networks of biochemical reactions. We apply this method to a cell cycle oscillator model. The reduced and hybridized model can be used as a hybrid model for the cell cycle. We also propose a practical recipe for detecting quasi-equilibrium QE reactions and quasi-steady state QSS(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)