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- Dima Grigoriev, Nicolai Vorobjov
- J. Symb. Comput.
- 1988

- Dima Grigoriev
- Theor. Comput. Sci.
- 2001

It is established a linear (thereby, sharp) lower bound on degrees of Positivstellensatz calculus refutations over a real eld introduced in GV99], for the Tseitin tautologies and for the parity (the mod 2 principle). We use the machinery of the Laurent proofs developped for binomial systems in BuGI 98], BuGI 99].

- Dima Grigoriev, Edward A. Hirsch, Dmitrii V. Pasechnik
- STACS
- 2001

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)

- Samuel R. Buss, Dima Grigoriev, Russell Impagliazzo, Toniann Pitassi
- J. Comput. Syst. Sci.
- 1999

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)

- Dima Grigoriev, Fritz Schwarz
- Computing
- 2004

- Dima Grigoriev, Nicolai Vorobjov
- Ann. Pure Appl. Logic
- 2001

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)

- Dima Grigoriev, Marek Karpinski, Michael F. Singer
- SIAM J. Comput.
- 1994

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)

- Dima Grigoriev
- Computational Complexity
- 2001

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)

- Vincent Noel, Dima Grigoriev, Sergei Vakulenko, Ovidiu Radulescu
- Electr. Notes Theor. Comput. Sci.
- 2012

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)

- Dima Grigoriev, Marek Karpinski, Michael F. Singer
- SIAM J. Comput.
- 1990

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)