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 Recursive information convertersA. V. Anisimov 3 Fundamental directions in the theory of homogeneous structuresV. B. Kudryavtsev, A. S. Podkolzin 19 Stability of a solution in a problem on the shortest path on a graphE. N. Gordeev 39 Extremal problems for $k$-colored graphs and unimprovable inequalities for pairs of random elementsA. F. Sidorenko 47 An upper bound on the capacity of the boundary of an antichain in an $n$-dimensional cubeA. V. Kostochka 53 The number of components in a random bipartite graphI. B. Kalugin 62 Circuits that allow short unit diagnostic testsN. P. Red'kin 71 Self-correction of schemes for some sequences of Boolean functionsN. I. Turdaliev 77 An asymptotic estimate for stratified finite populationsG. I. Ivchenko, S. A. Khonov 87 Finite initial segments of the upper semilattice of finite-automaton degreesS. S. Marchenkov 96 On the satisfiability fraction for formulas of $k$-valued logic with quantifiers min and maxV. V. Knyazev, V. A. Talanov 104 Complexity of self-correcting algorithms for two sorting problemsV. V. Morozenko 111 The structure of a random graph near a critical pointV. E. Britikov 121 Matroid decompositions of graphsR. I. Tyshkevich 129 The chromatic dimension of a graphT. G. Smirnova 139 The number of relations that determine classes of constants and selector functions of $k$-valued logicI. E. Bashtanov 141