ON ERROR PROBABILITY IN ONE MODEL OF COMPUTATION

Alekhina Marina Anatol'evna, Doctor of physical and mathematical sciences, professor, head of sub-department of discrete mathematics, Penza State University (40 Krasnaya street, Penza, Russia), alehina@pnzgu.ru

519.718

Background. Multivalued logic offers ample opportunities for development of various algorithms in many fields. It is successfully applied for solution of many problems and in many technical developments. These facts explain an interest to various models of computation, including circuits compiled of functional gates. The present work continues researching unreliability of circuits realizing functions of kmeaning logic (k ≥ 3); the aim of the work is to reveal properties of sub-circuits, error probability of which determines the lower value of unreliability of the whole circuit.
Materials and methods. The study was based on the well-known methods of discrete mathematics and mathematical cybernetics that provided values of circuit unreliability and allowed to assess a number of functions of special type.
Results. For a random k ≥ 3 the author has found sub-circuits, the error probability of which enables to assess reliability of the whole circuit, while the class of functions, realized by the said sub-circuits, has been significantly expanded. The previ-ously known class of such functions of four valued logic has been expanded in such a manner that any circuit, realizing the function of this class, holds the lower value of reliability in the Rosser-Turkett basis.
Conclusions. Error probability of some unreliable sub-circuits determines the lower value of unreliability of the whole system.

k-meaning logics functions, unreliable functional gates, synthesis of circuits composed of unreliable gates.

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