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ДНФ
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== Пример построения СДНФ для медианы==
=== Построение СДНФ для медианы от трех аргументов ===
1. В таблице истинности отмечаем те наборы переменных, на которых значение функции равно <tex> 1 </tex>.
<tex> \langle x,y,z \rangle = (x \land y \land z) \lor (\neg {x} \land y \land z) \lor (x \land \neg {y} \land z) \lor (x \land y \land \neg {z})</tex>.
=== Построение СДНФ для медианы от пяти аргументов ===
{| class="wikitable" style="width:16cm" border=1
|+
|-align="center" bgcolor=#EEEEFF
|<tex> x_1 </tex>||<tex> x_2 </tex>||<tex> x_3 </tex>||<tex>x_4</tex>||<tex> x_5 </tex>||<tex> \langle x_1, x_2, x_3, x_4, x_5 \rangle </tex> ||
|-align="center" bgcolor=#FFFFFF
| 0 || 0 || 0 || 0 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 0 || 0 || 0 || 1 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 0 || 0 || 1 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 0 || 0 || 1 || 1 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 0 || 1 || 0 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 0 || 1 || 0 || 1 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 0 || 1 || 1 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
! 0 || 0 || 1 || 1 || 1 || 1 || <tex>(\neg {x_1} \land \neg {x_2} \land x_3 \land x_4 \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
| 0 || 1 || 0 || 0 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 1 || 0 || 0 || 1 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 0 || 1 || 0 || 1 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
! 0 || 1 || 0 || 1 || 1 || 1 || <tex>(\neg {x_1} \land x_2 \land \neg {x_3} \land x_4 \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
| 0 || 1 || 1 || 0 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
! 0 || 1 || 1 || 0 || 1 || 1 || <tex>(\neg {x_1} \land x_2 \land x_3 \land \neg {x_4} \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
! 0 || 1 || 1 || 1 || 0 || 1 || <tex>(\neg {x_1} \land x_2 \land x_3 \land x_4 \land \neg {x_5})</tex>
|-align="center" bgcolor=#FFFFFF
! 0 || 1 || 1 || 1 || 1 || 1 || <tex>(\neg {x_1} \land x_2 \land x_3 \land x_4 \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
| 1 || 0 || 0 || 0 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 1 || 0 || 0 || 0 || 1 || 0 ||
|-align="center" bgcolor=#FFFFFF
| 1 || 0 || 0 || 1 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
! 1 || 0 || 0 || 1 || 1 || 1 || <tex>(x_1 \land \neg {x_2} \land \neg {x_3} \land x_4 \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
| 1 || 0 || 1 || 0 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
! 1 || 0 || 1 || 0 || 1 || 1 || <tex>(x_1 \land \neg {x_2} \land x_3 \land \neg {x_4} \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 0 || 1 || 1 || 0 || 1 || <tex>(x_1 \land \neg {x_2} \land x_3 \land x_4 \land \neg {x_5})</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 0 || 1 || 1 || 1 || 1 || <tex>(x_1 \land \neg {x_2} \land x_3 \land x_4 \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
| 1 || 1 || 0 || 0 || 0 || 0 ||
|-align="center" bgcolor=#FFFFFF
! 1 || 1 || 0 || 0 || 1 || 1 || <tex>(x_1 \land x_2 \land \neg {x_3} \land \neg {x_4} \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 1 || 0 || 1 || 0 || 1 || <tex>(x_1 \land x_2 \land \neg {x_3} \land x_4 \land \neg {x_5})</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 1 || 0 || 1 || 1 || 1 || <tex>(x_1 \land x_2 \land \neg {x_3} \land x_4 \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 1 || 1 || 0 || 0 || 1 || <tex>(x_1 \land x_2 \land x_3 \land \neg {x_4} \land \neg {x_5})</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 1 || 1 || 0 || 1 || 1 || <tex>(x_1 \land x_2 \land x_3 \land \neg {x_4} \land x_5)</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 1 || 1 || 1 || 0 || 1 || <tex>(x_1 \land x_2 \land x_3 \land x_4 \land \neg {x_5})</tex>
|-align="center" bgcolor=#FFFFFF
! 1 || 1 || 1 || 1 || 1 || 1 || <tex>(x_1 \land x_2 \land x_3 \land x_4 \land x_5)</tex>
|}
<tex> \langle x_1, x_2, x_3, x_4, x_5 \rangle = (\overline {x_1} \land \overline {x_2} \land x_3 \land x_4 \land x_5) \lor (\overline {x_1} \land x_2 \land \overline {x_3} \land x_4 \land x_5) \lor (\overline {x_1} \land x_2 \land x_3 \land \overline {x_4} \land x_5) \lor (\overline {x_1} \land x_2 \land x_3 \land x_4 \land \overline {x_5}) \lor (\overline {x_1} \land x_2 \land x_3 \land x_4 \land x_5) \lor (x_1 \land \overline {x_2} \land \overline {x_3} \land x_4 \land x_5) \lor (x_1 \land \overline {x_2} \land x_3 \land \overline {x_4} \land x_5) \lor (x_1 \land \overline {x_2} \land x_3 \land x_4 \land \overline {x_5}) \lor (x_1 \land \overline {x_2} \land x_3 \land x_4 \land x_5) \lor (x_1 \land x_2 \land \overline {x_3} \land \overline {x_4} \land x_5) \lor (x_1 \land x_2 \land \overline {x_3} \land x_4 \land \overline {x_5}) \lor (x_1 \land x_2 \land \overline {x_3} \land x_4 \land x_5) \lor (x_1 \land x_2 \land x_3 \land \overline {x_4} \land \overline {x_5}) \lor (x_1 \land x_2 \land x_3 \land \overline {x_4} \land x_5) \lor (x_1 \land x_2 \land x_3 \land x_4 \land \overline {x_5}) \lor (x_1 \land x_2 \land x_3 \land x_4 \land x_5)</tex>.
==Примеры СДНФ для некоторых функций==
Исключающее или: <tex> x \oplus y \oplus z = (\overline{x} \land \overline{y} \land z) \lor (\overline{x} \land y \land \overline{z}) \lor (x \land \overline{y} \land \overline{z}) \lor (x \land y \land z)</tex>.
== См. также ==
