Yuri Matiyasevich - Publications#

[1] (with Gleb Beliakov) Approximation of Riemann's zeta function by finite Dirichlet series: multiprecision numerical approach.
http://arxiv.org/abs/1402.5295, 2014.

[2] The Riemann Hypothesis and eigenvalues of related Hankel matrices. I. POMI Preprints 03/2014, 19 pages; available online: http://www.pdmi.ras.ru/preprint/2014/14-03.html.

[3] Calculation of Riemann's zeta function via interpolating determinants. Preprint 2013-18 of Max Planck Institute for Mathematics in Bonn; available online
http://www.mpim-bonn.mpg.de/preblob/5368, 2013.

[4] (with Gleb Beliakov) A parallel algorithm for calculation of large determinants with high accuracy for GPUs and MPI clusters.
http://arxiv.org/abs/1308.1536, 2013.

[5] (with Filip Saidak and Peter Zvengrowski) Horizontal monotonicity of the modulus of the riemann zeta function and related functions. http://arxiv.org/abs/1205.2773, 2012.

[6] New conjectures about zeroes of Riemann's zeta function. Research report MA12-03 of Department of Mathematics of University of Leicester, available online: http://www2.le.ac.uk/departments/mathematics/research/research-reports-2/reports-2012/ma12-03, 2012.

[7] Что можно и что невозможно делать с диофантовыми проблемами.
Труды МИАН, 275:128-143, 2011. English translation: What can and cannot be done with Diophantine problems, Proceedings of the Steklov Institute of Mathematics, volume 275, number 1, pages 118-132, 2011.

[8] Альтернативы формуле Эйлера-Маклорена для вычисления бесконечных сумм. Математические заметки, 88(4):543-548, 2010.
English translation: Alternatives to the Euler-Maclaurin formula for calculating infinite sums. Mathematical Notes, vol. 88, issue 4, pages 524-529, 2010; doi: 10.1134/S0001434610090245.

[9] Towards finite-fold Diophantine representations. Записки научных семинаров ПОМИ, 377:78-90, 2010. Reproduced in Journal of Mathematical Sciences (New York), vol 171, issue 6, pages 745-752, 2010; doi: 10.1007/s10958-010-0179-4.

[10] One more probabilistic reformulation of the four colour conjecture. Combinatorics, Probability and Computing, 19(5-6):829-834, 2010.

[11] (with Vesa Halava and Jarkko Kari) On Post correspondence problem for letter monotonic languages. Theoretical Computer Science, 410(30-32):2957-2960, 2009.

[12] Existential arithmetization of Diophantine equations. Ann. Pure Appl. Logic, 157(2-3):225-233, 2009. MR MR2499711.

[13] Computation paradigms in light of Hilbert's tenth problem. InS.Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors, New Computational Paradigms. Changing Conceptions of What is Computable, pages 59-86. Springer-Verlag, 2008. ISBN 978-0-387-36033-1.

[14] (with Patrick Cégielski and Irène Guessarian) Tree inclusion problems. Theor. Inform. Appl., 42(1):5-20, 2008. MR MR2382541 (2008m:68053). Zbl 1149.68040.

[15] Riemann's zeta function: More computations and conjectures. In Anatanas Laurinčikas and Jörn Steuding, editors, Voronoï's Impact on Modern Science. Proceedings of the 4th International Conference on Analytical Number Theory and Spacial Tesselations, pages 2-11. Drahomanov National Pedagogical University, Kiev, Ukraine, 2008.

[16] Riemann's zeta function: Some computations and conjectures. In Anne-Maria Ernvall-Hytönen, Matti Jutila, Juhani Karhumäki, and Arto Lepistö, editors, Proceedings of Conference on Algorithmic Number Theory 2007, pages 87-112, Turku, 2007. Available online: http://tucs.fi/publications/attachment.php?fname=G46.pdf.

[17] Hidden life of Riemann's zeta function 2. Electrons and trains. http://arXiv.org/abs/0709.0028, 2007. 2

[18] Hidden life of Riemann's zeta function 1. Arrow, bow, and targets. http://arXiv.org/abs/0707.1983, 2007.

[19] (with Patrick Cégielski and Irène Guessarian) Multiple serial episodes matching. Inform. Process. Lett., 98(6):211-218, 2006. MR 2221532 (2007m:68323).

[20] Diophantine flavor of Kolmogorov complexity. Transactions of the Institute for Informatics and Automation Problems of the National Academy of Sciences of Armenia, 27:111-122, 2006. ISSN 0131-4645.

[21] (with Patrick Cégielski, Irène Guessarian, and Yury Lifshits) Window subsequence problem for compressed texts. Lecture Notes in Computer Science, 3967:127-136, 2006. MR 2260988 (2007f:68231). Zbl 1178.68694.

[22] (with Géraud Sénizergues) Decision problems for semi-Thue systems with a few rules. Theoretical Computer Science, 330:145-169, 2005. MR 2112772 (2006c:03059). Zbl 1078.03033.

[23] Hilbert's tenth problem and paradigms of computation. Lecture Notes in Computer Science, 3526:310-321, 2005. Zbl 1115.03004.

[24] Some probabilistic restatements of the four color conjecture. J. Graph Theory, 46:166-179, 2004. MR 2063367 (2005d:05066). Zbl 1053.05050.

[25] Elimination of quantifiers from arithmetical formulas defining recursively enumerable sets. Mathematics and Computers in Simulation, 67:125-133, 2004. MR 2088903 (2005d:03057). Zbl 1073.6889.

[26] Один вероятностный эквивалент гипотезы четырех красок. Теория вероятностей и ее применения, 48:411-416, 2003. English translation: One probabilistic equivalent of the four color conjecture. Theory of Probability and Its Applications, 48(2):368-372, 2004. MR 2015463 (2004i:05056). Zbl 1052.05044.

[27] Диофантово представление чисел Бернулли и его приложения. Труды Математического института им. В.А.Стеклова РАН, 242:98-102, 2003. English translation: A Diophantine representation of Bernoulli numbers and its applications. Proc. Steklov Inst. Math., 2003. MR 2054487 (2005e:11028). Zbl 1118.11013.

[28] (with Luc Boasson, Patrick Cégielski and Irène Guessarian) Window-accumulated subsequence matching problem is linear. Annas Pure Applied Logic, 113:59-80, 2002. MR 1875736 (2003b:68082). Zbl 0998.68042.

[29] Некоторые алгебраические методы вычисления количества раскрасок графов. Записки научных семинаров ПОМИ АН СССР, 283:193-205, 2001. English translation: Some algebraic methods for calculating the number of colorings of a graph. J. Math. Sci., New York, 121(3):2401-2408, 2001. MR 1879070 (2002i:05046). Zbl 1063.05046.

[30] Some arithmetical restatements of the four color conjecture. Theoretical Computer Science, 257(1-2):167-183, 2001. MR 1825093 (2002f:03107). Zbl 0979.05049.

[31] Hilbert's tenth problem: What was done and what is to be done. Contemporary Mathematics, 270:1-47, 2000. MR 1802008(2001m:03084). Zbl 0994.03002.

[32] (with Volker Diekert and Anca Muscholl) Solving word equations modulo partial commutations. Theoretical Computer Science, 224:215-235, 1999. MR 1714796 (2001g:03023). Zbl 0930.68074.

[33] (with Maurice Margenstern) A binomial representation of the 3x+1 problem. Acta Arithmetica, 91(4):367-378, 1999. MR 1736018 (2001g:11015). Zbl 0968.11011.

[34] Hilbert's tenth problem: A two-way bridge between number and computer science. In C. S. Calude, editor, People and Ideas in Theoretical Computer Science, Springer series in discrete mathematics and theoretical computer science, pages 177-204. Springer-Verlag, Singapore, 1999. MR 1734859. Zbl 1125.11302.

[35] (with Volker Diekert and Anca Muscholl) Solving trace equations using lexicographical normal forms. Lecture Notes in Computer Science, 1256:336-347, 1997.

[36] Some decision problems for traces. Lecture Notes in Computer Science, 1234:248-257, 1997. MR 1616196. Zbl 980.17125.

[37] Mots et codes: Cas décidables et indécidables du problème du codage pour les monoïdes partialement commutatifs. Quadrature, 27:23-33, 1997. ISSN 1142-2785.

[38] Вычисление обобщенных полиномов Чебышева на компьютере. Вестник МГУ, 6:59-61, 1996. English translation: Computer evaluation of generalized Chebyshev polynomials. Mosc. Univ. Math. Bull., 51(6):39-40, 1996. Zbl 892.41017.

[39] (with Patrick Cegielski and Denis Richard) Definability and decidability issues in extensions of the integers with the divisibility predicate. Journal of Symbolic Logic, 61(2):515-540, 1996. Zbl 868.11061.

[40] (with Anatoli Degtyarev and Andrei Voronkov) Simultaneous rigid E-unification and related algorithmic problems. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science (LICS), pages 494-502, New Brunswick, New Jersey, 27-30 July 1996. IEEE Computer Society Press. MR 1461861.

[41] (with Géraud Sénizergues) Decision problems for semi-Thue systems with a few rules. In Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science (LICS), pages 523-531, New Brunswick, New Jersey, 27-30 July 1996. IEEE Computer Society Press. MR 1461864.

[42] Word problem for Thue systems with a few relations. Lecture Notes in Computer Science, 909:39-53, 1995. MR 1381720 (96k:03102).

[43] Новая техника для получения диофантовых представлений путем устранения ограниченных кванторов общности. Записки научных семинаров ПОМИ АН СССР, 220:83-92, 1995. English translation: A new technique for obtaining Diophantine representations via elimination of bounded universal quantifiers. J. Math. Sci., 87(1):3228-3233, 1997. MR 1374097 (97h:03071).

[44] Interval computations as propagation of constraints. In Brian Mayoh, Enn Tyugu, and Jaan Penjam, editors, Constraint programming: Proceedings of the NATO Advanced Study Institute on Constraint Programming, held Aug. 13-24, 1993 in Parnu, Estonia, volume 131 of NATO ASI series. Series F, Computer and systems science, pages 140-152, Berlin etc., 1994. Springer-Verlag. Zbl 810.65041.

[45] Les equations-bricoleurs. Revue de Mathematiques Speciales, 5:305-309, 1994. ISSN 0035-1504.

[46] A direct method for simulating partial recursive functions by Diophantine equations. Annals Pure Appl. Logic, 67(1-3):325-348, 1994. Zbl 795.03054.

[47] Десятая проблема Гильберта. Наука, Moscow, 1993. ISBN 5-02-014326-X. English edition: Hilbert's Tenth Problem. MIT Press, Cambridge, Massachusetts, 1993, ISBN 0-262-13295-8. French edition: Le dixième problème de Hilbert. Son indécidabilité. Masson, Paris, Milan, Barcelone, 1995, ISBN 2-225-84835-1. MR 1244324 (94m:03002b), 1247235 (94m:03002a). Zbl 0790.03008, 0790.03009.
Homepage of the book: http://logic.pdmi.ras.ru/~yumat/H10Pbook.

[48] (with J.P.Jones) Proof of recursive unsolvability of Hilbert's tenth problem. American Mathematical Monthly, 98:689-709, 1991. Zbl 746.03006.

[49] (with J.P.Jones) Basis for the polynomial time computable functions. In Mollin R. A. editor, Proc. First Conf. Canadian Number Theory Assoc., pages 255-270, Berlin etc, 1990. Walter de Gruyter. MR 1106666 (93d:03046). Zbl 693.03023.

[50] The Riemann Hypothesis from a logician's point of view. In R.A.Mollin, editor, Proc. First Conf. Canadian Number Theory Assoc., pages 387-400, Berlin ets, 1990. Walter de Gruyter. MR 1106674 (92f:11119). Zbl 697.10050.

[51] (with A.N.Terekhov and B.A.Fedotov) Унификация математического обеспечения для микроЭВМ на базе виртуальной машины. Автоматика и телемеханика, 5:168-175, 1990. English translation: Standardization of microcomputer software using virtual-machine design. Autom. Remote Control, 51(5):710-716, 1990. Zbl 800.68321.

[52] Связи между некоторыми суммами по тривиальным и нетривиальным нулям дзета-функции Римана. Математические заметки, 45(2):65-70, 1989. English translation: A relationship between certain sums over trivial and nontrivial zeros of the Riemann zeta function. Math. Notes, 45(1/2):131-135, 1989. MR 1002519 (90d:11099). Zbl 0663.10041.

[53] Диофантова сложность. Записки научных семинаров ЛОМИ АН СССР, 174:122-131, 1988. English translation: Diophantine complexity. Journal of Soviet Mathematics, 55(2):1603-1610, 1991. MR 976176 (90f:03078). Zbl 679.03016.

[54] Возможные нетрадиционные методы установления выполнимости пропозициональных формул. Вопросы кибернетики, 131:87-90, 1987. English translation: Possible nontraditional methods of establishing unsatisfability of propositional formulas. Amer. Math. Soc. Transl. Ser. 2, 178:75-77, 1997. MR 0931066 (89g:03013), 1423610.

[55] (with R. K. Guy) A new formula for рi. Amer. Math. Monthly, 93:631-635, 1986. MR MR1712797 (2000i:11199). Zbl 0614.10003.

[56] Вещественные числа и ЭВМ (Real numbers and computers). Кибернетика и вычислительная техника, 2:104-133, 1986.

[57] A posteriori version of interval analysis. In Proc Fourth Hungarian Computer Sci. Conf., pages 339-349. Budapest, 1986. MR 844351 (87i:65075).

[58] A posteriori interval analysis. Lecture Notes in Computer Science, 204:328-334, 1985. MR 826570. Zbl 0581.65031.

[59] Об исследованиям по некоторым алгоритмическим проблемам алгебры и теории чисел. Труды Матем. ин-та АН СССР, 168:218-235, 1984. English translation: On investigations of some algorithmic problems of algebra and number theory. Proc Steklov Inst. Math., 168(3):227-252, 1986. MR MR755902 (85k:01040). Zbl 597.03020.

[60] (with A.N. Terekhov) 16-разрядная виртуальная машина, ориентированная на АЯВУ (16-bit virtual computer oriented to high level programming languages). In Программирование микропроцессорной техники. Институт Кибернетики АН ЭССР, Таллин, 68-72, 1984.

[61] (with J.P.Jones) Register machine proof of the theorem on exponential Diophantine representation of enumerable sets. J. Symbolic Logic, 49:818-829, 1984. MR 758933 (85i:03139). Zbl 0599.03043.

[62] Одно аналитическое представление для суммы величин, обратных к нетривиальным нулям дзета-функции Римана. Труды Матем. ин-та АН СССР, 163:181-182, 1984. English translation: An analytic representation for the sum of reciprocals of the nontrivial zeros of the Riemann zeta-function. Proc. Steklov Inst. Math., 163:211-213, 1985. MR MR769884 (86d:11069). Zbl 551.10030.

[63] (with J.P.Jones) Direct translation of register machines into exponential Diophantine equations. In L. Priese, editor, Report First GFI Workshop Found. Theor. Computer Sci., pages 117-130. Univ. Gesamthochschule, Paderborn, 1983.

[64] Еще один машинный эксперимент в пользу гипотезы Римана. Кибернетика, 6:10,22, 1982. English translation: Yet another machine experiment in support of Riemann's Hypothesis. Cybernetics, 18(6):705-707, 1983. MR 716432 (85g:11079). Zbl 0516.10032.

[65] (with J.P.Jones) A new representation for the symmetric binomial coefficient and its applications. Ann. Sci. Math. Quebec, 6:81-97, 1982. MR 84g:03060. Zbl 499.03028.

[66] (with J.P.Jones) Exponential Diophantine representation of recursively enumerable sets. Studies in Logic and Foundations of Mathematics, 107:159-177, 1982. MR 85i:03138.

[67] What should we do having proved a decision problem to be unsolvable? Lecture Notes in Computer Science, 122:441-443, 1981.

[68] Алгоритмическая неразрешимость экспоненциально диофантовых уравнений с тремя неизвестными. In Теория алгорифмов и математическая логика, A.A.Markov and V.I.Homich, eds, Moscow, 69-78, 1979. English translation: Algorithmic unsolvability of xponential Diophantine equations in three unknowns. Selecta Math. Sovietica, 3(3):223-232, 1983/84. MR 81f:03055, 81b:03003.

[69] Some purely mathematical results inspired by mathematical logic. In Proc. Fifth Intern. Congr. Logic, Methodology and Philos. of Sci. (London, Ont., 1975), pages 121-127, Dordrecht, 1977. Reidel. MR 58, #5508.

[70] Простые числа перечисляются полиномом от 10 переменных. Записки научных семинаров ЛОМИ АН СССР, 68:62-82, 1977. English translation: Primes are non-negative values of a polynomial in 10 variables. J. Soviet Math., 15:33-44, 1981. Zbl 446.10046.

[71] Один класс критериев простоты, формулируемый в терминах делимости биномиальных коэффициентов. Записки научных семинаров ЛОМИ АН СССР, 67:167-183, 1977. English translation: A class of primality criteria formulated in terms of the divisibility of binomial coefficients. J. Soviet Math., 16(1):874-885, 1981. MR 57, #3060.

[72] Об одном представлении хроматического многочлена (On a repesentation of the chromatic polynomial). Дискретный анализ, 31:61-70, 1977. Zbl 435.05025. English translation: http://arXiv.org/abs/0712.1884.

[73] О задаче характеризации множества степеней данного числа в терминах остатков разложения квадратичных иррациональностей в цепную дробь (On the problem of chrachterization of the set of powers of a given number in terms of remainders of expansions of quadratic irrationalities into continuous fraction). In Цепные дроби и их применения. Киев, 75-76, 1976.

[74] Новое доказательство теоремы об экспоненциально диофантовом представлении перичислимых предикатов. Записки научных семинаров ЛОМИ АН СССР, 60:75-92, 1976. English translation: A new proof of the theorem on exponential Diophantine representation of enumerable sets. J. Soviet Math., 14(5):1475-1486, 1980. MR 58 #27402. Zbl 449.03043.

[75] (with M.Davis and J.Robinson) Hilbert's Tenth Problem. Diophantine equations: positive aspects of a negative solution. Proc. Symp. Pure Math., 28:323-378, 1976. MR 55 #5522.

[76] О метаматематическом подходе к задачам дискретной математики. Записки научных семинаров ЛОМИ АН СССР, 49:31-50, 1975. English translation: Metamathematical approach to proving theorems of discrete mathematics. J. Soviet Math., 10:517-533, 1978. MR 0376327 (51 #12503). Zbl 325.68048, Zbl 0401.68074.

[77] (with J.Robinson) Reduction of Diophantine equation to one in 13 unknowns. Acta Arithmetica, 27:521-553, 1975. MR 52 #8033.

[78] Один критерий раскрашиваемости вершин графа, формулируемый в терминах ориентаций ребер (A criteria of colorability of vertices of a graph stated in term of edge orientations). Дискретный анализ, 26:65-71, 1974. Zbl 298.05114. English translation: http://arXiv.org/abs/0712.1884.

[79] (with J.Robinson) Два универсальных трехкванторных представления перечислимых множеств (Two universal three-quantifier representations of enumerable sets). In Теория алгорифмов и математическая логика. ВЦ АН СССР, Москва, 112-123, 1974. English translation: http://arXiv.org/abs/0802.1052. MR 0406780 (53 #10566). Zbl 327.02035.

[80] Одна схема доказательств в дискретной математике. Записки научных семинаров ЛОМИ АН СССР, 40:94-100, 1974. English translation: A proof scheme in discrete mathematics. J. Soviet Math., 8:312-316, 1977. MR 0363823 (51 #78). Zbl 359.68106.

[81] Существование неэффективизируемых оценок в теорииэкспоненциально диофантовых уравнений. Записки научных семинаров ЛОМИ АН СССР, 40:77-93, 1974. English translation: Existence of noneffectivizable estimates in the theory of exponential Diophantine equations. Journal of Soviet Mathematics, 8(3):299-311, 1977. MR 0374025 (51 #10225). Zbl 361.02057.

[82] On recursive unsolvability of Hilbert's tenth problem. Studies in Logic and Found. of Math., 74:89-110, 1973. MR 0465823 (57 #5711).

[83] Арифметические представления перечислимых множеств с небольшим числом кванторов. Записки научных семинаров ЛОМИ АН СССР, 32:77-84, 1972. English translation: Arithmetical representation of enumerable sets with a small number of quantifiers. Journal of Soviet Math., 6(4):410-416, 1976. MR 49 #8835.

[84] Применение методов теории логического вывода в теории графов. Математические заметки, 12(6):781-790, 1972. English translation: The application of the methods of the theory of logical derivation to graph. Mathematical Notes, 12(1972)(6):904-908, 1973. MR 0321781 (48 #148). Zbl 0247.05115.

[85] Диофантовы множества. Успехи матем. наук, 27(5/176):185-222, 1972. English translation: Diophantine sets. Russian Math. Surveys, 27(5):124-164, 1972. Zbl 0269.02019.

[86] Диофантово представление перечислимых предикатов. Математические заметки, 12(1):115-120, 1972. English translation: Diophantine representation of enumerable predicates. Mathematical Notes, 12(1):501-504, 1972. Zbl 255.05104.

[87] (with W.W.Boone and D.J.Collins) Embeddings into semigroups with only a few defining relations. In J.E.Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, pages 27-40, Amsterdam, 1971. North-Holland. Zbl 0228.20029.

[88] Diophantine representation of recursively enumerable predicates. In J.E.Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, pages 171-177, Amsterdam, 1971. North-Holland. Zbl 0223.02042.

[89] Diophantine representation of recursively enumerable predicates. In Actes Congres Intern. Math. (Nice, 1970), pages 235-238, Paris, 1971. Gauthier-Villars. MR 54, #2444. Zbl 0235.02039.

[90] О распознавании в реальное время отношения вхождения. Записки научных семинаров ЛОМИ АН СССР, 20:104-114, 1971. English translation: Real-time recognition of the inclusion relation. Journal of Soviet Mathematics, 1(1):64-70, 1973. Zbl 253.02043.

[91] Достаточное условие сходимости монотонных последовательностей. Записки научных семинаров ЛОМИ АН СССР, 20:97-103, 1971. English translation: A sufficient condition for the convergence of monotone sequences. Journal of Soviet Mathematics, 1(1):59-63, 1973. Zbl 0252.02033.

[92] Диофантово представление множества простых чисел. Доклады АН СССР, 196(4):770-773, 1971. English translation: Diophantine representation of the set of prime numbers. Soviet Math. Doklady, 12(4):249-254, 1971. MR 43, #1921.

[93] Диофантово представление перечислимых предикатов. Известия АН СССР, сер. матем., 35(1):3-30, 1971. English translation: Diophantine representation of enumerable predicates. Math. of the USSR. Izvestija, 5[1971]:1-28, 1972. MR 43, #54. Zbl 0252.02047.

[94] Диофантовость перечислимых множеств. Доклады АН СССР, 191(2):279-282, 1970. English translation: Enumerable sets are Diophantine. Soviet Math. Dokl., 11:354-357, 1970. Hungarian

translation: (Solution of tenth problem of Hilbert). Mat. Lapok., 21:83-87, 1970. MR 41, #3390. Zbl 0212.33401. Reprinted in: Mathematical logic in the 20th century, Gerald E. Sacks, edt., Singapore University Press, Singapore; World Scientific Publishing Co., Inc., River Edge, NJ, 2003.

[95] Арифметические представления степеней. Записки научных семинаров ЛОМИ АН СССР, 8:159-165, 1968. English translation: Arithmetic representations of powers. Seminars in Mathematics, V.A.Steklov Mathematical Institute, 8:75-78, 1970. MR 39, #62. Zbl 0235.10012.

[96] Две редукции 10-й проблемы Гильберта. Записки научных семинаров ЛОМИ АН СССР, 8:145-158, 1968. English translation: Two reductions of Hilbert's Tenth Problem. Seminars in Mathematics, V.A.Steklov Mathematical Institute, 8:68-74, 1970. Zbl 0212.33302.

[97] Связь систем уравнений в словах и длинах с 10-й проблемой Гильберта. Записки научных семинаров ЛОМИ АН СССР, 8:132-144, 1968. English translation: The connection between Hilbert's Tenth

Problem and systems of equations between words and lengths.Seminars in Mathematics, V.A.Steklov Mathematical Institute, 8:61-67, 1970. MR 40, # 41. Zbl 0235.10012.

[98] Простые примеры неразрешимых канонических исчислений. Труды Матем. ин-та АН СССР, 93:50-88, 1967. English translation: Simple examples of unsolvable canonical calculi. Proc Steklov Inst. Math., 93:61-110, 1967. Zbl 0193.31801.

[99] Простые примеры неразрешимых ассоциативных исчислений. Доклады АН СССР, 173(6):1264-1266, 1967. English translation: Simple examples of undecidable associative calculi. Soviet Math. Dokl., 8:555-557, 1967. MR 36, #50. Zbl 0189.01102.