G. S. Makanin

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In this paper we construct an algorithm recognizing the solvability of arbitrary equations in a free semigroup. Bibliography: 4 titles. The study of equations in a free semigroup was begun by A. A. Markov. He constructed an algorithm recognizing the solvability of equations in two unknowns. Ju. I. Hmelevskii [1] constructed an algorithm recognizing the(More)
Classically, in order to resolve an equation u ≈ v over a free monoid X∗, we reduce it by a suitable family F of substitutions to a family of equations uf ≈ vf , f ∈ F , each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get F in a handy parametrized form. The method we propose consists(More)
In this article we introduce the functions Fi(x1, x2)λ1,..., λs and Th(x1, x2, x3)iλ1,..., λ2s (i = 1, 2, 3), of the word variables xi and of the natural number variables λi, where s ≥ 0. By means of these functions, we give exactly the general solution (i.e. the set of all the solutions) of the first basic parametric equation: x1x2x3x4 = x3x1λx2x5, in a(More)
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