Geodesic
On equations in free monoids and semigroups with~restrictions on solutions
Prikladnaâ diskretnaâ matematika, no. 1 (2023), pp. 5-19.

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We study algorithmic problems for equations in free monoids and semigroups (equations in words and lengths) with additional restrictions on the solutions. It is proved that it is impossible to construct an algorithm that solves an arbitrary system of equations in words and lengths in a free monoid (free semigroup) of rank 2 with an additional constraint on the solution in the form that one of its components belongs to the language of balanced words or the equality of the projections of two components of the solution into a distinguished free generator to determine whether it has a solution. A similar result is obtained for systems of inequalities in words.
Keywords: systems of equations in free monoids and free semigroups, equations in words and lengths, equations with restrictions on solutions. 
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V. G. Durnev; A. I. Zetkina. On equations in free monoids and semigroups with~restrictions on solutions. Prikladnaâ diskretnaâ matematika, no. 1 (2023), pp. 5-19. http://geodesic.mathdoc.fr/item/PDM_2023_1_a0/

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