Upper Bound of the Circuits Unreliability in a Complete Finite Basis (in P3) with Arbitrary Faults of Elements
- 3 Downloads
In this paper it is considered the implementation of ternary logic functions by the circuits of unreliable functional elements in an arbitrary complete finite basis. It is assumed that all the circuit elements pass to fault states independently of each other, and the faults can be arbitrary (for example, inverse or constant). Previously known class of ternary logic functions is extended, the circuits of these functions can be used to raise the reliability of the original circuits. With inverse faults at the outputs of basis elements it is constructively proved using functions of this class (we denote by G it) that a function which differs from any one of the variables can be implemented by a reliable circuit, and the probability of the inverse fault is bounded above by a constant. In particular if the basis under consideration contains at least one of the class G functions then for any function which differs from any one of the variables the constructed circuit is not only reliable, but this one is asymptotically optimal by reliability (we remind that function which is equal to one of the variables can be implemented absolutely reliably, not using functional element).
Keywords and phrasesternary logics functions unreliable functional elements synthesis of circuits composed of unreliable elements asymptotically optimal by reliability circuits inverse faults at the outputs of elements
Unable to display preview. Download preview PDF.
- 1.Yu. Vinogradov, “Synthesis of triple-MOS circuits,” in Mathematical Problems of Cybernetics, Collection of Articles, Ed. by S. V. Yablonskii (Nauka, Moscow, 1991), Vol. 3, pp. 187–198 [in Russian].Google Scholar
- 3.J. von Neuman, “Probabilistic logics and the synthesis of reliable organisms from unreliable components,” in Automata studies, Ed. by C. Shannon and J. McCarthy (Princeton Univ. Press, Princeton, 1956), pp. 43–98.Google Scholar
- 9.M. Alekhina and S. Kargin, “Asymptotically optimal reliable circuits in RosserЦTurkett basis in P 4,” Izv. Vyssh. Uchebn. Zaved., Povolzh. Region, Fiz. Mat. Nauki 1, 37–53 (2015).Google Scholar
- 12.O. Barsukova, “The synthesis of reliable circuitswhich realizes binary and ternary logics functions,” Extended Abstract of Cand. Sci. (Phys. Math.) Dissertation (Kazan State Univ., Kazan, 2014).Google Scholar
- 13.O. Lupanov, Asymptotic Estimates of the Complexity of Control Systems (Mosk. Gos. Univ., Moscow, 1984) [in Russian].Google Scholar
- 15.S. Yablonskii, Introduction into Discrete Mathematics (Nauka, Moscow, 2001) [in Russian].Google Scholar