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Studying algorithmic problems for free semi-groups and groups

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1234))

Abstract

In this paper we study some algorithmic problems for free semi-groups and groups.

Supported by the grant # 96-01-00525 of the Russian Foundation for Fundamental Research

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References

  1. Adian S. I., Makanin G. S., Investigations on algorithmic questions on algebra, Trudy Matematicheskogo Instituta Akademii Nauk SSSR. V. 168. Algebra, mathematical logics, theory of numbers, topology. Sbornik obzornyh statey. 1. K 50-letiyu Instituta. Moscow: Nauka, 1984. P.197–217.

    Google Scholar 

  2. Beltyukov A. P., Solvability of universal theory of natural numbers with addition and divisibility, Zapiski hauchnyh seminarov LOMI Akademii Nauk SSSR. 1976. V. 60, N 7. P. 15–28.

    Google Scholar 

  3. Durnev V. G., Positive theory of free semi-group, Doklady Akademii Nauk SSSR. 1973. V. 211, N 4. P.772–774.

    Google Scholar 

  4. Durnev V. G., About equtions on free semi-groups and groups, Mathematicheskie zametki. 1974. V. 16, N 5. P.717–724.

    Google Scholar 

  5. Durnev V. G., About equations with endomorphisms in free semi-groups, Diskretnaya mathematika. 1992. V. 4, N 2. P.136–141.

    Google Scholar 

  6. Durnev V. G., About equations with restrictions on solutions in free groups, Mathematicheskie zametki. 1993. V. 53, N 1. P.36–40.

    Google Scholar 

  7. Durnev V. G., About equations with semi-group restrictions on solutions in free groups, Diskretnaya mathematika. 1995. V.7, N 4. P.60–67.

    Google Scholar 

  8. Durnev V. G., Unsolvability of positive ∀∃3-theory of free semi-group, Sibirsky mathematichesky jurnal. 1995. V.36, N 5. P. 1067–1080.

    Google Scholar 

  9. Durnev V. G., To problem of solvability of equations with one coefficient, Mathematicheskie zametki. 1996. V. 59, N 6. P.832–846.

    Google Scholar 

  10. Kosovsky N. K., Elements of mathematical logic and its application to theory of sub-recursive algorithms. Leningrad: Izdatelstvo Leningradskogo Gosudarstvennogo Universiteta, 1981. 192 p.

    Google Scholar 

  11. Makanin G. S., Problem of solvability of equations in free semi-group, Mathematichesky sbornik. 1977. V. 103, N 2. P.147–236.

    Google Scholar 

  12. Makanin G. S., Equations in free groups, Izvestiya Akademii Nauk SSSR. Seriya mathematiki. 1982. V. 46, N 6. P.1199–1274.

    Google Scholar 

  13. Marchenkov S. S., Unsolvability of positive ∀∃-theory of free semi-group, Sibirsky mathematichesky jurnal. 1982. V.23, N 1. P.196–198.

    Google Scholar 

  14. Myacnikov A. G., Remeslennikov V. N., Elementary equivalence of free products of groups with length function in signature, X Vsesoyuzniy simpozium po teorii grupp. Tezisy dokladov. Minsk, 1986. P. 160.

    Google Scholar 

  15. Myacnikov A. G., Remeslennikov V. N., Elementary equivalence of free products. Sibirskoe otdelenie Akademii Nauk SSSR, VC, Preprint N 718. Novosibirsk, 1987. 20 p.

    Google Scholar 

  16. Repin N. N., Certain simply defined groups for which an algorithm recognizing solvability of equations is impossible, Boprocy kibernetiki. Slojnoct vychisleniy i prikladnaya mathematicheskaya logika. Moscow, 1988. P.167–174.

    Google Scholar 

  17. Romankov V. A., About unsolvability of problem of endomorphic reducibility in free nilpotent groups and in free rings, Algebra i logika. 1977. V. 16, N 4. P.457–471.

    Google Scholar 

  18. Taytslin M. A., Some examples of unsolvable theories, Algebra i logika. 1967. V.6, N 3. P.105–111.

    Google Scholar 

  19. Taytslin M. A., About algorithmic problem for coomutative semi-groups, Doklady Akademii Nauk SSSR. 1968. V. 178, N 4. P.786–789.

    Google Scholar 

  20. Hmelevsky Yu. I., Systems of equations in free group, Izvestiya Akademii Nauk. Seriya mathematiki. 1971. V. 35, N 6. P.1237–1268.

    Google Scholar 

  21. Büchi J. R., Senger S., Definability in the existential theory of concatenation and undecidable extensions of this theory, Z. Math. Log. und Grundl. Math. 1988. Bd 34, N 4. P. 337–342.

    Google Scholar 

  22. Büchi J. R., Senger S., Coding in the existential theory of concatenation, Arch. Math. Logik. 1986/87. Bd 26. P. 101–106.

    Google Scholar 

  23. Lipshitz L., The Diophantine problem for addition and divisibility, Trans. Amer. Math. Soc. 1978. V. 235. P. 271–283.

    Google Scholar 

  24. Lyndon R. C., Dependence in groups, Colloq. Math. 1966. N 4. P. 275–283.

    Google Scholar 

  25. Quine W., Concatenation as a basis for arithmetic, J. Symbolic Logic. 1946. V.11. P. 105–114.

    Google Scholar 

  26. Schupp P.E., On the substitution problem for free groups, Proc. Amer. Math. Soc. 1969. V. 23, N 2. P. 421–423.

    Google Scholar 

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Sergei Adian Anil Nerode

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© 1997 Springer-Verlag Berlin Heidelberg

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Durnev, V. (1997). Studying algorithmic problems for free semi-groups and groups. In: Adian, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 1997. Lecture Notes in Computer Science, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63045-7_10

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  • DOI: https://doi.org/10.1007/3-540-63045-7_10

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  • Print ISBN: 978-3-540-63045-6

  • Online ISBN: 978-3-540-69065-8

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