Asymptotically optimal reliable circuits in Rosser–Turkett basis (in P k )

Synthesis of reliable circuits in the basis consisting of the Webb function in Pk

“…Ïðè ïðîèçâîëüíîì k ≥ 3 çàäà÷à ñèíòåçà íàäåaeíûõ ñõåì, òî÷íåå àñèìïòîòè÷åñêè îïòèìàëüíûõ ïî íàäåaeíîñòè ñõåì, ðåøåíà òîëüêî â áàçèñå ÐîññåðàÒóðêåòòà è äâîéñòâåííîì åìó áàçèñå ïðè íåèñïðàâíîñòÿõ äâóõ âèäîâ: 1) èíâåðñíûõ íåèñïðàâíîñòÿõ, êîòîðûå õàðàêòåðèçóþòñÿ òåì, ÷òî íà êàaeäîì âõîäíîì íàáîðå ëþáîãî èç áàçèñíûõ ýëåìåíòîâ âåðîÿòíîñòü ïîÿâëåíèÿ íåâåðíîãî çíà÷åíèÿ íà âûõîäå ýëåìåíòà îäèíàêîâà [7]; 2) ïðè êîíñòàíòíûõ íåèñïðàâíîñòÿõ òèïà 0 è òèïà k − 1 íà âûõîäàõ ýëåìåíòîâ [8].  ýòèõ áàçèñàõ ïðè íàçâàííûõ íåèñïðàâíîñòÿõ äëÿ ïîâûøåíèÿ íàäåaeíîñòè èñõîäíûõ ñõåì èñïîëüçîâàëàñü îäíà è òà aeå ñõåìà èç òðåõ ýëåìåíòîâ ãëóáèíû 2, à â ðàññìàòðèâàåìîì áàçèñå B (è B * ) íàéäåíû äâå ñõåìû, êîòîðûå ìîaeíî èñïîëüçîâàòü äëÿ ïîâûøåíèÿ íàäåaeíîñòè èñõîäíûõ.…”