Structural implementation of discrete functions and estimates of its complexity
Graph embedding and structural modeling in some computational models
Questions of completeness and expressiveness for some types of functional systems
Problems of hashing and compressing information
Mathematical problems of VLSI design
Main publications:
S. A. Lozhkin, V. S. Zizov, “Asimptoticheski tochnye otsenki dlya ploschadi multipleksorov v modeli kletochnykh skhem”, Diskret. matem., 2022, 52-68
S. A. Lozhkin, D. S. Kinzhikeeva, “O strukture, slozhnosti i glubine skhem v bazise {&,∨}, realizuyuschikh stupenchatye funktsii algebry logiki”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 2020, 335-349
S. A. Lozhkin, “On the Depth of a Multiplexer Function with a Small Number of Select Lines”, Mat. Zametki, 115:5 (2024), 741–748; Math. Notes, 115:5 (2024), 748–754
2022
2.
S. A. Lozhkin, V. S. Zizov, “Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model”, Diskr. Mat., 34:4 (2022), 52–68; Discrete Math. Appl., 34:2 (2024), 103–115
3.
S. A. Lozhkin, “Refined bounds on Shannon’s function for complexity of circuits of functional elements”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 3, 32–40; Moscow University Mathematics Bulletin, 77:3 (2022), 144–153
2020
4.
S. A. Lozhkin, D. S. Kinzhikeyeva, “On the structure, complexity, and depth of the circuits over the basis $\{ \&, \vee\} $ realizing step Boolean functions”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 162:3 (2020), 335–349
5.
S. A. Lozhkin, V. S. Zizov, “Refined estimates of the decoder complexity in the model of cellular circuits with functional and switching elements”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 162:3 (2020), 322–334
V. V. Zhukov, S. A. Lozhkin, “Asymptotically best method for synthesis of Boolean recursive circuits”, Diskr. Mat., 31:1 (2019), 99–110; Discrete Math. Appl., 30:2 (2020), 137–146
S. A. Lozhkin, M. S. Shupletsov, B. R. Danilov, “Synthesis of asymptotically size-optimal Boolean circuits protected from functionality inference”, Mat. Vopr. Kriptogr., 8:2 (2017), 87–96
S. A. Lozhkin, V. A. Konovodov, “Fine precision estimation of Boolean formulas' complexity in some bases consisting of gates with direct and iterative inputs”, University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 2, 16–31
9.
S. A. Lozhkin, V. A. Konovodov, “On logic algebra formulas' complexity in some complete bases consisting of elements with both direct and iterative inputs”, University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 1, 54–67
S. A. Lozhkin, M. S. Shupletsov, “Switching activity of Boolean circuits and synthesis of Boolean circuits with asymptotically optimal complexity and linear switching activity”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 156:3 (2014), 84–97
S. A. Lozhkin, V. A. Konovodov, “Complexity of realization of Boolean functions from some classes related to finite grammars by formulas of alternation depth $3$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 3, 14–19; Moscow University Mathematics Bulletin, 69:3 (2014), 100–105
2009
12.
S. A. Lozhkin, N. V. Vlasov, “On Multiplexer Function Complexity in the $\pi$-schemes Class”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 151:2 (2009), 98–106
S. A. Lozhkin, “Synthesis of formulas whose complexity and depth do not exceed the asymptotically best estimates of high degree of accuracy”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2007, no. 3, 19–25
S. A. Lozhkin, M. A. Koshkin, “Complexity of the realization of some systems of Boolean functions
by multiterminal switching circuits”, Dokl. Akad. Nauk SSSR, 298:4 (1988), 807–811; Dokl. Math., 37:1 (1988), 162–166
17.
S. A. Lozhkin, A. A. Semenov, “On a method for compressing information and on the complexity of the realization of monotone symmetric functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, no. 7, 44–52; Soviet Math. (Iz. VUZ), 32:7 (1988), 73–85
S. A. Lozhkin, “Asymptotic behavior of Shannon functions for the delays of schemes of functional elements”, Mat. Zametki, 19:6 (1976), 939–951; Math. Notes, 19:6 (1976), 548–555
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