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
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
Durnev V. G., Positive theory of free semi-group, Doklady Akademii Nauk SSSR. 1973. V. 211, N 4. P.772–774.
Durnev V. G., About equtions on free semi-groups and groups, Mathematicheskie zametki. 1974. V. 16, N 5. P.717–724.
Durnev V. G., About equations with endomorphisms in free semi-groups, Diskretnaya mathematika. 1992. V. 4, N 2. P.136–141.
Durnev V. G., About equations with restrictions on solutions in free groups, Mathematicheskie zametki. 1993. V. 53, N 1. P.36–40.
Durnev V. G., About equations with semi-group restrictions on solutions in free groups, Diskretnaya mathematika. 1995. V.7, N 4. P.60–67.
Durnev V. G., Unsolvability of positive ∀∃3-theory of free semi-group, Sibirsky mathematichesky jurnal. 1995. V.36, N 5. P. 1067–1080.
Durnev V. G., To problem of solvability of equations with one coefficient, Mathematicheskie zametki. 1996. V. 59, N 6. P.832–846.
Kosovsky N. K., Elements of mathematical logic and its application to theory of sub-recursive algorithms. Leningrad: Izdatelstvo Leningradskogo Gosudarstvennogo Universiteta, 1981. 192 p.
Makanin G. S., Problem of solvability of equations in free semi-group, Mathematichesky sbornik. 1977. V. 103, N 2. P.147–236.
Makanin G. S., Equations in free groups, Izvestiya Akademii Nauk SSSR. Seriya mathematiki. 1982. V. 46, N 6. P.1199–1274.
Marchenkov S. S., Unsolvability of positive ∀∃-theory of free semi-group, Sibirsky mathematichesky jurnal. 1982. V.23, N 1. P.196–198.
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.
Myacnikov A. G., Remeslennikov V. N., Elementary equivalence of free products. Sibirskoe otdelenie Akademii Nauk SSSR, VC, Preprint N 718. Novosibirsk, 1987. 20 p.
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.
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.
Taytslin M. A., Some examples of unsolvable theories, Algebra i logika. 1967. V.6, N 3. P.105–111.
Taytslin M. A., About algorithmic problem for coomutative semi-groups, Doklady Akademii Nauk SSSR. 1968. V. 178, N 4. P.786–789.
Hmelevsky Yu. I., Systems of equations in free group, Izvestiya Akademii Nauk. Seriya mathematiki. 1971. V. 35, N 6. P.1237–1268.
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.
Büchi J. R., Senger S., Coding in the existential theory of concatenation, Arch. Math. Logik. 1986/87. Bd 26. P. 101–106.
Lipshitz L., The Diophantine problem for addition and divisibility, Trans. Amer. Math. Soc. 1978. V. 235. P. 271–283.
Lyndon R. C., Dependence in groups, Colloq. Math. 1966. N 4. P. 275–283.
Quine W., Concatenation as a basis for arithmetic, J. Symbolic Logic. 1946. V.11. P. 105–114.
Schupp P.E., On the substitution problem for free groups, Proc. Amer. Math. Soc. 1969. V. 23, N 2. P. 421–423.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-63045-7_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63045-6
Online ISBN: 978-3-540-69065-8
eBook Packages: Springer Book Archive