Множество существенных импликант

T =

;

01x11 S^a = 8, S^b = 10.

0111x

г) Выбор минимального покрытия.

1. Метод Петрика.

Y = (C v D) (A v E) (C v E) (F v G) (C v D v F v G v H) (E v F) (B v I) (D v I) (A v B) (G v I) (D v G v H v I) = (C v DE) (A v EB) (G v FI) (D v G v H v CI v FI) (E v F) (I v BD) = (CA v CED v DEA v DEB) (GI v GBD v FI v FBD )(DE v GE v HE v CIE v FIE v DF v GF v HF v CIF v FI) = (CAGI v CAGBD v CAFI v CAFBD v CEDGI v CEDGB v CEDFI v CEDFB v DEAGI v DEAGB v DEAFI v DEAFB v DEBCI v DEG v DEBFI v DEBF) (DE v GE v HE v CIE v FIE v DF v GF v HF v CIF v FI) = (CAGI v CAGBD v CAFI v CAFBD v CEDFI v DEAFI v DEBCI v DEG v DEBF) (DE v GE v HE v CIE v FIE v DF v GF v HF v FI) = ACFI v BDEG v BDEFI v BCEFI v ACEGI v BCEGI v ADEFI v ADEGI v ABCDFG v …

Минимальные покрытия функции :

1)

Cmin(f) =

T A C = F I

01x11 0111x 1x010 10xx1 101xx 11x0x

S^a = 21, S^b = 27.

_ _ _ _ _ _ _

ƒ = X₁X₂X₄X₅ v X₁X₂X₃X₄ v X₁X₃X₄X₅ v X₁X₂X₅ v X₁X₂X₃ v X₁X₂X₄ ;

Cmin(f) =

T B D = E G

01x11 0111x 110x0 1xx01 10x1x 1x10x

S^a = 21, S^b = 27.

_ _ _ _ _ _ _

ƒ = X₁X₂X₄X₅ v X₁X₂X₃X₄ v X₁X₃X₄X₅ v X₁X₄X₅ v X₁X₂X₄ v X₁X₃X₄ ;

Cmin(f) =

T B D = E F I

01x11 0111x 110x0 1xx01 10x1x 101xx 11x0x

S^a = 24, S^b = 31.

_ _ _ _ _ _ _ _

ƒ = X₁X₂X₄X₅ v X₁X₂X₃X₄ v X₁X₃X₄X₅ v X₁X₄X₅ v X₁X₂X₄ v X₁X₂X₃ v X₁X₂X₄ ;

Cmin(f) =

T B C = E F I

01x11 0111x 110x0 10xx1 10x1x 101xx 11x0x

S^a = 24, S^b = 31.

_ _ _ _ _ _ _ _

ƒ = X₁X₂X₄X₅ v X₁X₂X₃X₄ v X₁X₃X₄X₅ v X₁X₂X₅ v X₁X₂X₄ v X₁X₂X₃ v X₁X₂X₄ ;

Cmin(f) =

T A C = E G I

01x11 0111x 1x010 10xx1 10x1x 1x10x 11x0x

S^a = 24 S^b = 31.

_ _ _ _ _ _ _ _

ƒ = X₁X₂X₄X₅ v X₁X₂X₃X₄ v X₁X₃X₄X₅ v X₁X₂X₅ v X₁X₂X₄ v X₁X₃X₄ v X₁X₂X₄ ;

3.2 б) Нахождение простых имплицент.

N	Ko(ƒ) N(ƒ)	*	N	K1(ƒ)		*	N	K2(ƒ)		*	N	K3(ƒ)		*	N	Z(ƒ)
1	00000	*	1	0000x	1-2	*	1	000xx	1-9	*	1	00xxx	1-10		1	x0000
2	00001	*	2	000x0	1-3	*	2	00x0x	1-13	*	2	0xx0x	2-14		2	11x11
3	00010	*	3	00x00	1-5	*	3	0x00x	1-21	*					3	1111x
4	00011	*	4	0x000	1-9	*	4	00xx0	2-14	*					4	0x0x0
5	00100	*	5	x0000	1-15		5	0x0x0	2-22						5	0x1x1
6	00101	*	6	000x1	2-4	*	6	0xx00	3-23	*					6	xx111
7	00110	*	7	00x01	2-6	*	7	00xx1	6-16	*					7	00xxx
8	00111	*	8	0x001	2-10	*	8	0xx01	7-24	*					8	0xx0x
9	01000	*	9	0001x	3-4	*	9	00x1x	9-18	*
10	01001	*	10	00x10	3-7	*	10	001xx	13-18	*
11	01010	*	11	0x010	3-11	*	11	0x10x	13-25	*
12	01101	*	12	00x11	4-8	*	12	0x1x1	16-26
13	01111	*	13	0010x	5-6	*	13	xx111	19-28
14	10000	*	14	001x0	5-7	*	14	01x0x	21-25	*
15	11011	*	15	0x100	5-12	*
16	11110	*	16	001x1	6-8	*
17	11111	*	17	0x101	6-13	*
18	11101	*	18	0011x	7-8	*
19	11111	*	19	0x111	8-14	*
			20	x0111	8-16	*
			21	0100x	9-10	*
			22	010x0	9-11	*
			23	01x00	9-12	*
			24	01x01	10-13	*
			25	0110x	12-13	*
			26	011x1	13-14	*
			27	x1111	14-19	*
			28	1x111	16-19	*
			29	11x11	17-19
			30	1111x	18-19

б) Составление имплицентной таблицы.

		00000	00001	00010	00011	00100	00101	00110	01000	01001	01010	01100	01101	10000	11011	11110
	#	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
x0000	1	*												*
11x11	2														*
1111x	3															*
0x0x0	4	*		*					*		*
0x1x1	5						*						*
xx111	6
00xxx	7	*	*	*	*	*	*	*			*			*
0xx0x	8	*	*			*	*		*	*		*	*