#### Filter Results:

- Full text PDF available (117)

#### Publication Year

1978

2017

- This year (5)
- Last 5 years (40)
- Last 10 years (57)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn 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].

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

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

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… (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)

- 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
- J. Symb. Comput.
- 1988

- 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 Philippon. These bounds are sharp, as well as they are for the Nullstellensatz refutations… (More)

- Dima Grigoriev
- J. Symb. Comput.
- 1990

- Dima Grigoriev, Marek Karpinski
- AAECC
- 1993

Recall that a polynomial f 2 FX1; : : : ; Xn] is t-sparse, if f = P IX I contains at most t terms. In BT 88], GKS 90] (see also GK 87] and Ka 89]) the problem of interpolation of t-sparse polynomial given by a black-box for its evaluation has been solved. In this paper we shall assume that F is a eld of characteristic zero. One can consider a t-sparse… (More)