Abstract:
A survey of definitions of the rank of a coefficientless equation in a free semigroup is given. An algorithm is constructed which for every equation in four unknowns in a free semigroup discerns whether the rank of the equation is three or less than three.
Bibliography: 5 titles.
\Bibitem{Mak76}
\by G.~S.~Makanin
\paper On the rank of coefficientless equations in four unknowns in a~free semigroup
\jour Math. USSR-Sb.
\yr 1976
\vol 29
\issue 2
\pages 257--280
\mathnet{http://mi.mathnet.ru/eng/sm2875}
\crossref{https://doi.org/10.1070/SM1976v029n02ABEH003667}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=419645}
\zmath{https://zbmath.org/?q=an:0361.20060}
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Linking options:
https://www.mathnet.ru/eng/sm2875
https://doi.org/10.1070/SM1976v029n02ABEH003667
https://www.mathnet.ru/eng/sm/v142/i2/p285
This publication is cited in the following 5 articles:
S. I. Adian, “On the studies of Gennadii Semënovich Makanin on algorithmic questions of the theory of groups and semigroups”, Russian Math. Surveys, 73:3 (2018), 553–568
Taimanov A. Taimanov V., “On the Representation of the Solution of Equation in Free Semigroup Without Unit”, 312, no. 2, 1990, 274–276
Habib Abdulrab, Jean-Pierre Pécuchet, “Solving word equations”, Journal of Symbolic Computation, 8:5 (1989), 499
J.P Pecuchet, “Solutions principales et rang d'un système d'équations avec constantes dans le monoïde libre”, Discrete Mathematics, 48:2-3 (1984), 253
G. S. Makanin, “Recognition of the rank of equations in a free semigroup”, Math. USSR-Izv., 14:3 (1980), 499–545
Citation in format AMSBIB
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