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

- 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)

- 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].

- Alexander L. Chistov, Dima Grigoriev
- MFCS
- 1984

- 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, 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, Fritz Schwarz
- Computing
- 2004

The problem of factoring a linear partial differential operator is studied. An algorithm is designed which allows one to factor an operator when its symbol is separable, and if in addition the operator has enough right factors then it is completely reducible. Since finding the space of solutions of a completely reducible operator reduces to the same for its… (More)

- Dima Grigoriev
- computational complexity
- 2001

A lower bound is established on degrees of Positivstellensatz calculus refutations (over a real field) introduced in (Grigoriev & Vorobjov 2001; Grigoriev 2001) for the knapsack problem. The bound depends on the values of coefficients of an instance of the knapsack problem: for certain values the lower bound is linear and for certain values the upper bound… (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)