А. Шень - Публикации

2012

Ромащенко А.Е., Шень А., Дюран Б., B.Durand, A.Romashchenko, A.Shen. Fixed-point tile sets and their applications. Journal of Computer and System Sciences. Volume 78, Issue 3, May 2012, pp. 731-764. Electronic version: arXiv:0802.2432v3 (2009), http://arxiv.org/abs/0910.2415 http://arxiv.org/abs/0910.2415

2011

Ромащенко А.Е., Шень А., Мусатов Д.В., D.Musatov, A.Romashchenko, A.Shen. Variations on Muchnik"s Conditional Complexity Theorem. Theory Comput. Syst. 49 (2). 2011, pp. 227-245. Electronic version: arXiv:0904.3116v4, http://arxiv.org/abs/0904.3116 http://arxiv.org/abs/0904.3116

2009

Durand B., Romashchenko A., Shen A., Fixed point theorem and aperiodic tilings, Bulletin of the European Association for Theoretical Computer Science (EATCS), no. 97, pp. 126-136 (The Logic in Computer Science Column by Yuri Gurevich) http://www.eatcs.org/images/bulletin/beatcs97.pdf
Durand B., Romashchenko A., Shen A., High Complexity Tilings with Sparse Errors. In Proceedings: Automata, Languages and Programming, 36th International Colloquium, (ICALP), Rhodes, Greece, July 5-12, 2009. Part I. Lecture Notes in Computer Science 5555 Springer 2009, pp. 403-414.
Musatov D., Romashchenko A., Shen A., Variations on Muchnik"s Conditional Complexity Theorem. Lecture Notes in Computer Science 5675: Proc. 4th International Computer Science Symposium in Russia (CSR). Novosibirsk, Russia, August 18-23, 2009. pp. 250-262. Electronic version: arXiv:0904.3116v2, http://arxiv.org/abs/0904.3116 http://arxiv.org/abs/0904.3116
Гельфанд И.М., Шень А., Algebra (Textbook). Birkhauser, 1993, 2nd printing, 1995, 3rd printing, 2000, 4th printing, 2002, 5th printing, 2003, 6th printing, 2004. Русский вариант: Гельфанд И.М., Шень А. Алгебра. (Книга для школьников) Москва. МЦНМО, 2-е изд., 2009
Шень А., Космография. М.:МЦНМО, 2009
Shen A., Algorithmic Information Theory and Foundations of Probability Reachability Problems Third International Workshop, RP 2009, Palaiseau, France, September 23-25, 2009, Proceedings Lecture Notes in Computer Science Vol. 5797
Bienvenu L., Shafer G., Shen A., On the history of martingales in the study of randomness, Journal Elecronique d"Histoire des Probabilites et de la Statistique, ISSN 1773-0074.
Bienvenu L., Shen A., Algorithmic information theory and martingales. [A historic account] arxiv 0906.2614
Chernov A., Shen A., Muchnik An., Algorithmic randomness and splitting of supermartingales, arxiv 0807.3156 Проблемы передачи информации, 2009, 45:1, 60-70. English version: Problems of Information Transmission, 2009, 45:1, 54-64.
Bienvenu L., Muchnik An., Shen A., Verehshchagin N., Limit complexities revisited. Proceedings of STACS 2008 conference, p.73-84, http://drops.dagstuhl.de/opus/volltexte/2008/1335 Theory of Computing Systems, DOI 10.1007/s00224-009-9203-9, 17 March 2009. http://drops.dagstuhl.de/opus/volltexte/2008/1335

2008

Durand B., Romashchenko A., Shen A., Fixed Point and Aperiodic Tilings. Lecture Notes in Computer Science 5257 Springer: Proc. 12th international conference on Developments in Language Theory (DLT). Kyoto, Japan, September 2008, pp. 537-548. Electronic version: arXiv:0802.2432v3. http://arxiv.org/abs/0802.2432
Биенвеню Л., Ромащенко А.Е., Шень А., Laurent Bienvenu, Andrei Romashchenko, and Alexander Shen. Sparse sets. In Proc. First Symposium on Cellular Automata "Journees Automates Cellulaires" (JAC), Uzes, France, April 21-25, 2008, pp.18-28.
Верещагин Н.К., Шень А., Лекции по математической логике и теории алгоритмов. Часть 3. Вычислимые функции. М. МЦНМО. 2008 (3-е изд.) English version: N.Vereshchagin, A.Shen. Computable functions. Published by AMS, 2003. MR 2004b:03002
Верещагин Н.К., Шень А., Лекции по математической логике и теории алгоритмов. Часть 2. Языки и исчисления. М. МЦНМО. 2008 (3-е изд.)
Верещагин Н.К., Шень А., Лекции по математической логике и теории алгоритмов. Часть 1. Начала теории множеств. М. МЦНМО. 2008 (3-е изд.) English version: N.Vereshchagin, A.Shen. Basic set theory. Published by AMS, 2002. MR 2003f:03001
Шень А., Вероятность: примеры и задачи. М.:МЦНМО, 2007. 2-е издание, 2008
Bienvenu L., Merkle W., Shen A., A simple proof of Miller--Yu theorem. Fundamenta Informaticae, vol. 83, no. 1--2 (2008), p.21-24.
Vovk V., Shen A., Prequential Randomness, Algorithmic Learning Theory, 19th International Conference (ALT 2008), Budapest, Hungary, Oct. 13--16, 2008, p.~154--168.
Chernov A., Shen A., Vereshchagin N., Vovk V., On-line Probability, Complexity and Randomness. Algorithmic Learning Theory, 19th International Conference (ALT 2008), Budapest, Hungary, Oct. 13--16, 2008, Lecture Notes in Computer Science, v.~5254, p.~138--153.

2007

Шень А., Программирование: теоремы и задачи. Третье издание: МЦНМО, 2007. English version: "Algorithms and Programming: Problems and Solutions" published by Birkhauser in 1997. 2nd ed. 2008 (Modern Classics, Birkhauser), 3rd ed. 2009 (Springer).
Alon N., Newman I., Shen A., Tardos G., Vereshchagin N., Partitioning multi-dimensional sets in a small number of ``uniform"" parts. ECCC Report, TR05-95, European Journal of Combinatorics, Volume 28, Issue 1, January 2007, p. 134--144. doi:10.1016/j.ejc.2005.08.002 MR2261810
Шень А., A.Muchnik, A.Shen, N.Vereshchagin, M.Vyugin. Non-reducible descriptions for conditional Kolmogorov complexity. ECCC Report, TR04-054, Jun 29, 2004 See also: Theory and Applications of Models of Computation, Lecture Notes in Computer Science, Springer Berlin/Heidelberg, 3959 (2006), p.308-317 (a talk given in Beijing conference, May 2006). MR2277252 Extended version: Andrej Muchnik, Alexander Shen, Mikhail Ustinov, Nikolai Vereshchagin, Michael Vyugin, Non-reducible descriptions for conditional Kolmogorov complexity. Theoretical Computer Science, 2007, 384 (1), 77--86.
Шень А., Игры и стратегии. М.:МЦНМО, 2007. 2-е издание, 2008

2006

Шень А., Multisource information theory ECCC Report, TR06-006. Also published: Dagstuhl seminar 06051, http://drops.dagstuhl.de/opus/volltexte/2006/626 See also: Theory and Applications of Models of Computation, Lecture Notes in Computer Science, Springer Berlin/Heidelberg, 3959 (2006), p. 327-338. (a talk given in Beijing conference, May 2006). MR2277254
Шень А., О "математической строгости" и школьном курсе математики. М.:МЦНМО, 2006. 72с. ISBN 5-94057-254-5

2005

Шень А., B.Durand, L.A.Levin, A.Shen. Local rules and global order, or Aperiodic Tilings. Mathematical Intelligencer, 2005, v. 27, no.1, p. 64-68. MR 2006c:52058
Шень А., Простые и составные числа. М.:МЦНМО, 2005. 2-е изд., 2008
Шень А., Логарифм и экспонента. М.:МЦНМО, 2005.

2004

Шень А., Математическая индукция. М.:МЦНМО, 2004. 3-е изд., 2008

2002

Чернов А., Мучник Ан.А., Шень А., Ромащенко А.Е., Верещагин Н.К., Chernov A., Muchnik An., Shen A., Romashchenko A., Vereshchagin N. Upper semi-lattice of binary strings with the relation "x is simple conditional to y". Theoretical Computer Science. 271 (2002) pp. 69-95.
Ромащенко А.Е., Шень А., Верещагин Н.К., A.Romashchenko, A.Shen, N.Vereshchagin. Combinatorial Interpretation of Kolmogorov Complexity. Theoretical Computer Science. 271 (2002) pp. 111-123.
Шень А., А.Китаев, М.Вялый, А.Шень. Классические и квантовые вычисления. М.:МЦНМО, 1999 English translation by Lester J. Senechal: A. Kitaev, M. Vyalyi, A. Shen. Classical and quantum computations. AMS, RI, 2002. NR2003e:81004
Шень А., Верещагин Н., Logical operations and Kolmogorov complexity ECCC-088, 2001; Theoretical Computer Science, 271 (1--2), p. 125--129 (2002) MR 2002k:68080
Шень А., A. Romashchenko, A. Shen, N. Vereshchagin, Combinatorial interpretation of Kolmogorov complexity, ECCC 7(26):2000; 15th Annual IEEE conference on Computational Complexity (Florence, 2000), 131-137, IEEE Computer Soc., Los Alamitos, CA, 2000; MR1823533. TCS 271 (1--2): p. 111--123 (2002). MR 2003d:68104

2000

Хаммер Д., Ромащенко А.Е., Шень А., Верещагин Н.К., D.Hammer, A.Romashchenko, A.Shen, N.Vereshchagin. Inequalities for Shannon Entropy and Kolmogorov Complexity. Journal of Computer and System Sciences. 60 (2000) pp. 442-464. http://www.mccme.ru/~anromash/ps/hrsv2000.ps
Шень А., Задачи по математике, предлагавшиеся ученикам математического класса 57 школы (выпуск 2000 года, класс В). М.:МЦНМО, 2000.

1999

Muchnik An., Romashchenko A., Shen A., Vereshchagin N., Muchnik An., Romashchenko A., Shen A., Vereshchagin N. Upper Semilattice of Binary Strings with the Relation "x is Simple Conditional to y". Proceedings of the 14th Annual IEEE Conference on Computational Complexity, 4-6 May 1999, Atlanta, Georgia, USA. IEEE Computer Society. 114-121.

1997

Hammer D., Romashchenko A., Shen A., Vereshchagin N., Hammer D., Romashchenko A., Shen A., Vereshchagin N. Inequalities for Shannon entropies and Kolmogorov complexities. Proceedings of the Twelfth Annual IEEE Conference on Computational Complexity, June 24-27, 1997, Ulm, Germany. IEEE Computer Society Press. pp. 13-23

1992

Шень А., IP=PSPACE: simplified proof. Journal of the ACM, 39, no.4 (Oct. 1992), p. 878--880. MR 94j:68270

1990

Шень А., В.А.Успенский, А.Л.Семёнов, А.Шень, Может ли индивидуальная последовательность нулей и единиц быть случайной? - Успехи математических наук, 1990, 45(1), 105--162. Translation: V.A.Uspensky, A.L.Semenov, A.Shen. Can a single sequence of zeros and ones be random? Russian Math. Surveys, 45:1 (1990), 121--189. MR 91f:03043

1985

Шень А., Алгоритмические варианты понятия энтропии. Диссертация на соискание учёной степени кандидата физико-математических наук. Москва, 1985. (Russian)