Квантовые вычисления со времен Демокрита - Скотт Ааронсон - Страница 125

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R. Santhanam, Circuit lower bounds for Merlin — Arthur classes. SIAM Journal on Computing, 39:3 (2009), 1038–61.

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S. Aaronson and A. Wigderson, Algebrization: a new barrier in complexity theory. ACM Transactions on Computing Theory, 1:1 (2009), 2:1–54.

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M. L. Furst, J. B. Saxe, and M. Sipser, Parity, circuits, and the polynomial-time hierarchy. Mathematical Systems Theory, 17:1 (1984), 13–27.

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M. Ajtai. Sigma_1ˆ1-formulae on finite structures. Annals of Pure and Applied Logic, 24 (1983), 1–48.

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A. A. Razborov, On themethod of approximations. In Proceedings ofACMSymposium on Theory of Computing (New York: ACM, 1989), pp. 167–76.

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R. Smolensky, Algebraic methods in the theory of lower bounds for Boolean circuit complexity. In Proceedings of ACM Symposium on Theory of Computing (New York: ACM, 1987), pp. 77–82.

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A. A. Razborov and S. Rudich, Natural proofs. Journal of Computer and System Sciences, 55:1 (1997), 24–35.

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M. Naor and O. Reingold, Number-theoretic constructions of efficient pseudo-random functions. Journal of the ACM, 51:2 (2004), 231–62.

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R. Williams, Non-uniform ACC circuit lower bounds. In Proceedings of IEEE Conference on Computational Complexity (Silver Springs, MD: IEEE Computer Society Press, 2011), pp. 115–25.

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Более подробно см.: K. Mulmuley, The GCT program toward the P vs. NP problem. Communications of the ACM, 55:6 (2012), 98–107, http://ramakrishnadas.cs.uchicago.edu/, или прекрасную докторскую диссертацию Joshua Grochow, Symmetry and equivalence relations in classical and geometric complexity theory. Doctoral dissertation, University of Chicago (2012). http://people.cs.uchicago.edu/~joshuag/grochow-thesis.pdf).

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http://www.cpsc.ucalgary.ca/~jwatrous/papers/qip2.ps

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R. Jain, Z. Ji, S. Upadhyay, and J. Watrous, QIP = PSPACE. Journal of the ACM, 58:6 (2011), 30.

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A. Kitaev and J. Watrous, Parallelization, amplification, and exponential time simulation of quantum interactive proof systems. In Proceedings of Annual ACM Symposium on Theory of Computing (New York: ACM, 2000), pp. 608–17.

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Начиная с этой главы мы включили в текст некоторые диалоги со студентами, слушавшими данный курс.

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См., напр.: Nick Bostrom, Anthropic Bias: Observation Selection Effects in Science and Philosophy, Routledge, 2010.

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См., напр.: John Leslie, The End of the World: The Science and Ethics of Human Extinction, Routledge, 1998.

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Об аргументе Судного дня существует обширная литература. Хорошим началом служат уже упомянутые книги Бострома и Лесли, рано как и статья http://en.wikipedia.org/wiki/Doomsday_argument.

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J. R. Gott III, Implications of the Copernican principle for our future prospects. Nature, 363:6427 (1993), 315–319.

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http://math.ucr.edu/home/baez/week246.html

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BPPpath был введен в работе Y. Han, L. A. Hemaspaandra, and T. Thierauf, Threshold computation and cryptographic security. SIAM Journal on Computing, 26:1 (1997), 59–78.

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L. M. Adleman, J. DeMarrais, and M.-D. A. Huang, Quantum computability. SIAM Journal on Computing, 26:5 (1997), 1524–40.

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S. Aaronson, Quantum computing, postselection, and probabilistic polynomial-time. Proceedings of the Royal Society A, 461:2063 (2005), 3473–82. http://arxiv.org/abs/quant-ph/0412187

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R. Beigel, N. Reingold, and D. A. Spielman, PP is closed under intersection. Journal of Computer and System Sciences, 50:2 (1995), 191–202.

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M. Bremner, R. Jozsa, and D. Shepherd, Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy. Proceedings of the Royal Society A, 467:2126 (2010), 459–72. http://arxiv.org/abs/1005.1407

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S. Aaronson and A. Arkhipov, The computational complexity of linear optics. In Proceedings of Annual ACM Symposium on Theory of Computing (2011), pp. 333–42. http://arxiv.org/abs/1011.3245

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В самом деле, когда проводилась финальная редактура американского издания этой книги, четыре группы в области квантовой оптики объявили о первых успешных демонстрациях предложенной нами с Архиповым «бозонной выборки», хотя пока лишь с тремя идентичными фотонами. См. дополнительную информацию http://www.scottaaronson.com/blog/?p=1177.

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См., например, http://law2.umkc.edu/faculty/projects/ftrials/leoploeb/leopold.htm

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http://www.complexityzoo.com

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R. Nozick, Newcomb's problem and two principles of choice. In Essays in Honor of Carl G. Hempel, ed. N. Rescher, Synthese Library, Dordrecht, the Netherlands. (1969), pp. 114–115.

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После того как я прочитал эти лекции в 2006 г., я узнал, что Рэдфорд Нил независимо от меня предложил сходную идею. См.: R. M. Neal, Puzzles of anthropic reasoning resolved using full non-indexical conditioning, http://www.cs.toronto.edu/~radford/ftp/anth.pdf

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B. W. Libet, Do we have free will? Journal of Consciousness Studies, 6 (1999), 47–57.

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C. S. Soon, M. Brass, H.-J. Heinze, and J.-D. Haynes, Unconscious determinants of free decisions in the human brain. Nature Neuroscience, 11 (2008), 543–45.

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http://arxiv.org/abs/quant-ph/0604079

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http://www.scottaaronson.com/papers/nks.pdf

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S. Wolfram, A New Kind of Science, Wolfram Media, 2002.

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S. Pironio, A. Acın, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, Random numbers certified by Bell's

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