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Nicolai Vorobjov

Prof

  • 1 WEST 3.62

20012019

Research output per year

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Research Output

A Helly-type theorem for semi-monotone sets and monotone maps

Basu, S., Gabrielov, A. & Vorobjov, N., Dec 2013, In : Discrete & Computational Geometry. 50, 4, p. 857-864 8 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Approximation of definable sets by compact families, and upper bounds on homotopy and homology

Gabrielov, A. & Vorobjov, N., Aug 2009, In : Journal of the London Mathematical Society. 80, 1, p. 35-54 20 p.

Research output: Contribution to journalArticle

16 Citations (Scopus)

Betti numbers of semialgebraic and sub-Pfaffian sets

Gabrielov, A., Vorobjov, N. & Zell, T., 2004, In : Journal of the London Mathematical Society. 69, p. 27-43 17 p.

Research output: Contribution to journalArticle

22 Citations (Scopus)

Betti numbers of semialgebraic sets defined by quantifier-free formulae

Gabrielov, A. & Vorobjov, N., 2005, In : Discrete & Computational Geometry. 33, 3, p. 395-401 7 p.

Research output: Contribution to journalArticle

17 Citations (Scopus)

Bounds on sizes of finite bisimulations of Pfaffian dynamical systems

Korovina, M. & Vorobjov, N., 1 Dec 2008, In : Theory of Computing Systems. 43, 3-4, p. 498-515 18 p.

Research output: Contribution to journalArticle

Complexity of computations with Pfaffian and Noetherian functions

Vorobjov, N. & Gabrielov, A., 2004, Normal Forms, Bifurcations and Finiteness Problems in Differential Equations. Ilyashenko, Y. & Rousseau, C. (eds.). Springer, p. 211 1 p. (NATO Science Series II).

Research output: Chapter in Book/Report/Conference proceedingChapter

Complexity of cylindrical decompositions of sub-Pfaffian sets

Gabrielov, A. & Vorobjov, N., 2001, In : Journal of Pure and Applied Algebra. 164, 1-2, p. 179-197 19 p.

Research output: Contribution to journalArticle

14 Citations (Scopus)

Complexity of null- and Positivstellensatz proofs

Grigoriev, D. & Vorobjov, N., 2002, In : Annals of Pure and Applied Logic. 113, 1-3, p. 153-160 8 p.

Research output: Contribution to journalArticle

44 Citations (Scopus)

Effective model completeness of the theory of restricted Pfafflan functions

Vorobjov, N., 2003, Computer Science Logic, Proceedings. Vol. 2803. p. 544-544 1 p. (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceedingChapter

Effective quantifier elimination over real closed fields

Vorobjov, N., 2003, Computer Science Logic, Proceedings. Vol. 2803. p. 545-545 1 p. (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceedingChapter

Monotone functions and maps

Basu, S., Gabrielov, A. & Vorobjov, N., 2013, In : Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 107, 1, p. 5-33 29 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

New Complexity bounds for cylindrical decompositions of sub_Pfaffian sets

Vorobjov, N. & Pericleous, S., 2003, Discrete and Computational Geometry. Aronov, B. (ed.). Springer

Research output: Chapter in Book/Report/Conference proceedingChapter

New Complexity bounds for cylindrical decompositions of sub_Pfaffian sets

Vorobjov, N. & Pericleous, S., 2001.

Research output: Contribution to conferencePaper

On irreducible components of real exponential hypersurfaces

Vorobjov, N. & Riener, C., 10 Sep 2017, In : Arnold Mathematical Journal. 3, 3, p. 423-443 20 p.

Research output: Contribution to journalArticle

Open Access
File
80 Downloads (Pure)

On the number of homotopy types of fibres of a definable map

Basu, S. & Vorobjov, N., 2007, In : Journal of the London Mathematical Society. 76, p. 757-776 20 p.

Research output: Contribution to journalArticle

8 Citations (Scopus)

On topological lower bounds for algebraic computation trees

Gabrielov, A. & Vorobjov, N., 1 Feb 2017, In : Foundations of Computational Mathematics. 17, 1, p. 61-72 12 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Orthogonal tropical linear prevarieties

Vorobjov, N. & Grigoriev, D., 2018, Computer Algebra in Scientific Computing - 20th International Workshop, CASC 2018, Proceedings. Koepf, W., Seiler, W. M., Gerdt, V. P. & Vorozhtsov, E. V. (eds.). Springer, Vol. 11077. p. 187-196 10 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 11077 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Pfaffian hybrid systems

Korovina, M. & Vorobjov, N., 2004, Computer Science Logic, Proceedings. Vol. 3210. p. 430-441 12 p. (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceedingChapter

9 Citations (Scopus)

Reachability in one-dimensional controlled polynomial dynamical systems

Korovina, M. & Vorobjov, N., 2012, Perspectives of systems informatics: 8th International Andrei Ershov Memorial Conference, PSI 2011, Novosibirsk, Russia, June 27-July 1, 2011, Revised Selected Papers. Clarke, E., Virbitskaite, I. & Voronkov, A. (eds.). Berlin: Springer, p. 251-261 11 p. (Lecture Notes in Computer Science; vol. 7162).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Semi-monotone sets

Basu, S., Gabrielov, A. & Vorobjov, N., 2013, In : Journal of the European Mathematical Society. 15, 2, p. 635-657 23 p.

Research output: Contribution to journalArticle

7 Citations (Scopus)

The complexification and degree of a semi-algebraic set

Roy, M. F. & Vorobjov, N., 2002, In : Mathematische Zeitschrift. 239, 1, p. 131-142 12 p.

Research output: Contribution to journalArticle

10 Citations (Scopus)

Topological lower bounds for arithmetic networks

Gabrielov, A. & Vorobjov, N., 30 Sep 2017, In : Computational Complexity. 26, 3, p. 687-715 29 p.

Research output: Contribution to journalArticle

Open Access
File
105 Downloads (Pure)

Triangulations of monotone families I: two-dimensional families

Basu, S., Gabrielov, A. & Vorobjov, N., 11 Nov 2015, In : Proceedings of the London Mathematical Society. 111, 5, p. 1013-1051 42 p.

Research output: Contribution to journalArticle

File
2 Citations (Scopus)
105 Downloads (Pure)

Upper and lower bounds on sizes of finite bisimulations of Pfaffian hybrid systems

Korovina, M. & Vorobjov, N., 2006, Logical Approaches to Computational Barriers, Proceedings. Vol. 3988. p. 267-276 10 p. (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Citations (Scopus)

Upper bounds on Betti numbers of tropical prevarieties

Grigoriev, D. & Vorobjov, N., 1 Apr 2018, In : Arnold Mathematical Journal. 4, 1, p. 127-136 10 p.

Research output: Contribution to journalArticle

Open Access
File
2 Citations (Scopus)
15 Downloads (Pure)