SYNTHESIS OF ASYMPTOTICALLY RELIABILITY-OPTIMAL NON BRANCHING PROGRAMMES IN THE BASIS {х₁ v х₂ , х₁ & х₂ , х₁ ,stop}  

Alekhina Marina Anatolyevna, Doctor of physico-mathematical sciences, professor, head of sub-department of discrete mathematics, Penza State University, alehina@pnzgu.ru
Zinovyeva Svetlana Mikhaylovna, Assistant, sub-department of discrete mathematics, Penza State University, dm@pnzgu.ru

519.95

We consider the problem of synthesis of optimal on reliability nobranching programs with conditional stop-operator at inverse faults on operator outputs in basis {х₁ v х₂ , х₁ & х₂ , х₁ ,stop}. We proved that in this basis it’s possible to realize all Boolean functions with asymptotically optimal on reliability programs with conditional stop-operator, and for functions x_i (i∈{1,2,...,n})these programs are absolutely reliable (contain no operators), and for remaining functions these programs work with unreliability asymptotically equal ε at ε → 0 (ε is a probability of the inverse fault on the operator output).

Boolean functions, nobraching programs, conditional stop-operator, synthesis, reliability.