Geodesic
On equations in free semigroups with certain constraints on their solutions
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XI, Tome 358 (2008), pp. 120-129

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It is shown that the solvability problem for equations in free semigroups with certain constraints on their solutions is algorithmically unsolvable. Bibl. – 23 titles. 
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     title = {On equations in free semigroups with certain constraints on their solutions},
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V. G. Durnev; O. V. Zetkina. On equations in free semigroups with certain constraints on their solutions. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XI, Tome 358 (2008), pp. 120-129. http://geodesic.mathdoc.fr/item/ZNSL_2008_358_a6/