Alekhina Marina Anatol'evna

Publications in Math-Net.Ru

1. About the reliability of circuits under failures of type $0$ at the outputs of elements in a complete finite basis containing some pairs of functions
   
   Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 7,  10–17
2. About the reliability of logic circuits in all complete bases with three-input elements and failures of zero type on their outputs
   
   Prikl. Diskr. Mat., 2020, no. 49,  98–107
3. Asymptotically optimal in unreliability circuits in the basis consisting of the Webb function in $P_3$ under faults of type $2$ at the outputs of elements
   
   Prikl. Diskr. Mat., 2020, no. 47,  22–29
4. Synthesis of reliable circuits in the basis consisting of the Webb function in $P_k$
   
   Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 7,  15–28
5. About the reliability of circuits with faults of type $0$ at the outputs of elements in the complete finite basis containing a special function
   
   Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 6,  85–88
6. On reliability of circuits with type 0 failures at elements outputs in a full finite basis containing a linear function of two variables and generalized disincent
   
   University proceedings. Volga region. Physical and mathematical sciences, 2019, no. 1,  56–62
7. Sufficient conditions for implementation of Boolean functions by asymptotically optimal on reliability circuits with the trivial estimate of unreliability in the case of faults of type $0$ at the element outputs
   
   Prikl. Diskr. Mat., 2019, no. 45,  44–54
8. About reliability of circuits in the basis consisting of the Webb function in $P_k$ under failures of 0 type and $k-1$ type at the outputs of elements
   
   Prikl. Diskr. Mat., 2019, no. 44,  58–66
9. On the arbitrarily reliable implementation of Boolean functions by non-branching programs with a conditional stop operator in bases with generalized conjunction
   
   Prikl. Diskr. Mat., 2019, no. 43,  70–77
10. Asymptotically optimal in reliability circuits in two bases under failures of $0$ ($k-1$) type at the outputs of elements
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 5,  3–12
11. Recurrent relationships for unreliabilities of circuits with single-type constant malfunctions of types $0$ and ($k-1$) in the basis consisting from a web function, in $P_{k}$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2018, no. 4,  78–83
12. Upper estimate of unreliability of schemes in full finite basis (in $P_2$) for arbitrary faults of gates
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 12,  80–83
13. On a circuit that increases reliability in the basis consisting of a Webb function, at $P_{k}$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2017, no. 4,  70–75
14. Relaibility of dual circuits in $P_{k}$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2017, no. 1,  3–13
15. Estimations of unreliability of circuits in Rosser–Turkett basis (in $P_3$) with faults of type $0$ at the outputs of gates
    
    Prikl. Diskr. Mat., 2017, no. 37,  62–75
16. The unreliability of logic circuits of unreliable functional elements
    
    Prikl. Diskr. Mat. Suppl., 2017, no. 10,  128–130
17. On the reliability of circuits in some full bases (in $P_3$) with inverse faults at the gate outputs
    
    Prikl. Diskr. Mat. Suppl., 2017, no. 10,  126–128
18. The reliability of circuits in Rosser–Turkett basis (in $P_3$) with faults of type $0$ at the outputs of gates
    
    Prikl. Diskr. Mat. Suppl., 2017, no. 10,  124–126
19. On reliability of circuits in a basis “anticonjunction” with constant faults at the input gates
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 7,  3–9
20. On circuits being asymptotically optimal by reliability in cases of gate failures
    
    University proceedings. Volga region. Physical and mathematical sciences, 2016, no. 4,  60–67
21. Recurrent correlations for unreliabilities of circuits in the basis consisting of Webb functions, in $P_4$ and $P_5$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2016, no. 3,  19–30
22. Synthesis of reliable circuits at linear adhesion of variables in the “anticonjuction” basis
    
    University proceedings. Volga region. Physical and mathematical sciences, 2016, no. 1,  63–70
23. The unreliability of circuits in case coalescences of elements inputs
    
    Prikl. Diskr. Mat. Suppl., 2016, no. 9,  98–100
24. On the reliability of circuits in the Rosser–Tourkett basis (in $P_k$)
    
    Prikl. Diskr. Mat. Suppl., 2016, no. 9,  96–98
25. Upper bound of unreliability of circuits in a basis consisting of Webb function
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 3,  15–27
26. On error probability in one model of computation
    
    University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 4,  12–19
27. Synthesis of circuits containing unreliable gates in $P_k$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 3,  3–10
28. Synthesis of reliable circuits at constant failures at gates' inputs and outputs
    
    University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 2,  5–15
29. Asymptotic reliability-optimal circuits in the Кosser-Еurkett basis in $P_4$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 1,  37–53
30. Lower bounds for unreliability of circuits in the Rosser–Tourkett basis
    
    Prikl. Diskr. Mat. Suppl., 2015, no. 8,  104–105
31. A lower bound for unreliability of circuits in the Webb basis
    
    Prikl. Diskr. Mat. Suppl., 2015, no. 8,  102–103
32. Unreliability of circuits in case of constant failures on inputs and outputs of gates
    
    Prikl. Diskr. Mat. Suppl., 2015, no. 8,  100–102
33. On reliability of circuits realizing ternary logic functions
    
    Diskretn. Anal. Issled. Oper., 21:4 (2014),  12–24
34. On synthesis of unreliable element circuits in $P_4$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2014, no. 4,  47–56
35. Sythesis and complexity of cellular circuitry asymptotically optimal by reliability
    
    University proceedings. Volga region. Physical and mathematical sciences, 2014, no. 4,  5–16
36. Circuit failure estimate in the Rosser - Turkett basis
    
    University proceedings. Volga region. Physical and mathematical sciences, 2014, no. 1,  5–19
37. On Bases with Unreliability Coefficient $2$
    
    Mat. Zametki, 95:2 (2014),  170–201
38. The reliability of circuits in the basis of unreliable and absolutely reliable gates
    
    Prikl. Diskr. Mat. Suppl., 2014, no. 7,  111–112
39. Unreliability of circuits in the basis by Rosser–Turkett
    
    Prikl. Diskr. Mat. Suppl., 2014, no. 7,  109–110
40. On unreliability of functional elements circuits with two types of faults
    
    University proceedings. Volga region. Physical and mathematical sciences, 2013, no. 3,  31–47
41. On the issue of the elements number in the gate, realizing the generalized voting function
    
    University proceedings. Volga region. Physical and mathematical sciences, 2013, no. 2,  5–16
42. About unreliability bounds for circuit with inverse faults and functional element breakdowns
    
    Prikl. Diskr. Mat. Suppl., 2013, no. 6,  50–51
43. On reliability of circuits over an arbitrary complete finite basis under single-type constant faults at outputs of elements
    
    Diskr. Mat., 24:3 (2012),  17–24
44. Reliability of nonbranching programs in an arbitrary complete finite basis
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 2,  13–22
45. On the reliability of schemes implementing functions from $P_3$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 1,  57–65
46. Lower estimation of unreliability of non-branching programs with conditional stop operator
    
    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 1,  44–56
47. Sufficient conditions for realizability of Boolean functions by asymptotically optimal circuits with the unreliability $2\varepsilon$
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 5,  79–82
48. On asymptotically optimal reliability schemes in some special bases
    
    University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 4,  3–13
49. On reliability of circuits over the bases $\{\sim,\&,\oplus\}$, $\{\sim,\&,0\}$, $\{\oplus,\&,1\}$, $\{\oplus,\vee,1\}$ in the case of faults of type 0 at the outputs of elements
    
    Diskr. Mat., 21:2 (2009),  102–111
50. On Reliability of Combinatorial Circuits in Bases Containing Functions with at Most Three Variables
    
    Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 151:2 (2009),  25–35
51. On schemes that are asymptotically best with respect to reliability in the basis $\{\&,\vee,^-\}$ with inverse faults at the inputs of elements
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 13:4 (2006),  3–17
52. On the reliability of schemes in the basis $\{x\vee y\vee z,x\mathbin{\&}y\mathbin{\&}z,\bar{x}\}$ with single-type constant faults at the inputs of the element
    
    Diskr. Mat., 18:1 (2006),  116–125
53. Reliability and complexity of schemes in the basis $\{x|y\}$ with inverse faults of elements
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 12:2 (2005),  3–11
54. On the complexity of reliable circuits consisting of unreliable elements with single-type constant faults
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 11:2 (2004),  3–17
55. On the reliability of schemes in the bases $\{\nrightarrow,\rightarrow\}$, $\{\rightarrow,\oplus\}$ with faults of type 0 at the outputs of the elements
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 11:1 (2004),  3–12
56. On the reliability of schemes in the bases $\{\rightarrow,\bar{}\ \}$ and $\{\rightarrow,0\}$ with faults of type 0 at the outputs of the elements
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 10:1 (2003),  3–13
57. Synthesis and complexity of reliable schemes in the basis $\{\&,\vee,\bar{}\,\}$ with single-type constant faults at the inputs of elements
    
    Diskr. Mat., 15:1 (2003),  98–109
58. Lower bounds for the reliability of schemes in some bases with single-type constant faults at the inputs of the elements
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 9:3 (2002),  3–28
59. On the reliability of schemes in the bases $\{x\mid y\}$, $\{x\downarrow y\}$ with single-type constant faults at the inputs of the elements
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 8:2 (2001),  3–14
60. On the reliability of schemes in the basis $\{\vee,\&,\bar{}\,\}$ with single-type constant faults at the inputs of elements
    
    Diskr. Mat., 13:3 (2001),  75–80
61. On the reliability of schemes consisting of unreliable functional elements with one-type constant faults at the element outputs
    
    Diskr. Mat., 5:2 (1993),  59–74
62. Reliability of schemes in the basis $\{x\& y,x\vee y,\bar x\}$ with one-type constant faults on the element outputs
    
    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1992, no. 6,  56–58
63. On the complexity of reliable networks from functional gates in the case of constant faults of the same type at the outputs of the gates
    
    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1992, no. 5,  79–81
64. Synthesis of reliable schemes of functional elements $x/y$ in the case of constant faults of the same type on outputs of elements
    
    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1991, no. 5,  80–83


65. Synthesis of asymptotically optimal non-branching programs in the basis of $\{x_1\vee x_2, x_1 \& x_2, \bar{x}_1, stop\}$
    
    University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 2,  60–67
66. On two methods for improving the reliability of circuits
    
    University proceedings. Volga region. Physical and mathematical sciences, 2008, no. 4,  17–25
67. About functions and circuits used to improve circuit reliability
    
    University proceedings. Volga region. Physical and mathematical sciences, 2008, no. 3,  30–38