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Статья
2017

Upper estimate of unreliability of schemes in full finite basis (in P 2) for arbitrary faults of gates


M. A. AlekhinaM. A. Alekhina, Yu. S. GusyninaYu. S. Gusynina, T. A. ShornikovaT. A. Shornikova
Русская математика
https://doi.org/10.3103/S1066369X17120088
Abstract / Full Text

We consider the realization of Boolean functions by circuits with unreliable functional gates in a complete finite basis. We assume that each gate of the circuit is exposed to arbitrarily faults, and the gates faults are statistically independent. We construct the circuits for all Boolean functions and get their upper bound of the unreliability, which depends on the “worst” (the most unreliable) of the basic gate.

Author information
  • Penza State Technological University, Baidukov passage 1a / Gagarin str. 1, Penza, 440039, RussiaM. A. Alekhina, Yu. S. Gusynina & T. A. Shornikova
References
  1. SelectedWorks of S. V. Yablonsky, V. B. Alekseev, V. I. Dmitriev (Eds.) (MAKS Press, Moscow, 2004) [in Russian].
  2. Alekhina, M. A. “Synthesis, Reliability and Complexity of Circuits With Unreliable Functional Gates”, Doctoral dissertation in Mathematics and Physics nauk (Penza, 2004) [in Russian].
  3. Alekhina, M. A., Vasin, A. V. “Sufficient Conditions for Realizability of Boolean Functions by Asymptotically Optimal Circuits with the Unreliability 2ε”, RussianMathematics 54, No. 5, 68–70 (2010).
  4. Alekhina, M. A., Grabovskaya, S. M. “Reliability of Nonbranching Programs in an Arbitrary Complete Finite Basis”, RussianMathematics 56, No. 2, 10–18 (2012).
  5. Aksyonov, S. I. “On the Circuits Reliability Over an Arbitrary Complete System of Functions With Inverse Faults at Gate Outputs”, Izv. VUZ. Povolzhskii Region. Estestv. Nauki 6, No. 21, 42–55 (2005) [in Russian].
  6. Alekhina, M. A., Vasin, A. V. “On Reliability of Combinatorial Circuits in Bases Containing Functions with at Most Three Variables”, Uchen. Zap. Kazansk. Univ. Ser. Fiz.-Mat. Nauki 151, No. 2, 25–36 (2009) [in Russian].
  7. Alekhina, M. A. “On Reliability of Circuits Over an Arbitrary Complete Finite Basis Under Single-Type Constant Faults at Outputs of Elements”, DiscreteMathematics and Applications 22, No. 4, 383–391 (2012).