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, -

, , 1 (1),

B 3 [2,1]. : 1) = 1 2) = 2.

= 1, B3 z = 2.

= 1,

W (x,, z) = W (1, 1, 2) = 4.

= 2, B3 z = 1.

= 1,

W (x,, z) = W (2, 1, 1) = 3.

1--

0.5 0.5,

, ,

4·0.5 + 3·0 . 5= 3.5.

, : = 1

	1	2	B3	4
	[1,1]	[1,2]	[2,1]	[2,2]
(1)	W(1,1,1)	W(1,1,1)	W(1,1,2)	W(1,1,2)
(2)	W(1,2,1)	W(1,2,1)	W(1,2,2)	W(1,2,2)

= 2

	2	2	4	4
	1	1	4	;
	1	1	4	4

	1		2	B3	4
	[1,1]	[1,2]		[2,1]	[2,2]
(1)	W(2,1,1)	W(2,1,2)		W(2,1,1)	W(2,1,2)
(2)	W(2,2,1)	W(2,2,2)		W(2,2,1)	W(2,2,2)
	3	0	3	0
	3	5	3	.
	3	5	3	5

141

				0.5	1	3.5		2
				1	2	3.5		.
				1	2	3.5		4.5


						,
			.					:
				1	(1)	1	[1,1].
						:
		SA* = [1			0];	SB *= [1		0 0 0].
		= 0.5.
		4.8.
1-						:		,	-
1,				2/3,		2		1/3.
	x = 1,		2-					y	-
		{1, 2},							1-
,		3-						z
	{1,2},			,
		1-						2-	.
	x = 2,		2-					y	-
		{1, 2},						1-	-
,	3-							z	-
{1,2},		,			.				,
			W(x,		, z),		,		-
.
								. 4.9.
		-2	4	1 -4		3	0 -3	-5
		1	2	1	2	1	2 1	2
						A		A
		1		2		1	B	2
							B
				1			2
								. 4.9
						142

						-
		y, z	,	( {1, 2})		2-
		y, z	,	( {1, 2})		2-

,	1-			x = 1, z (z {1,2})
3-	,	1-		x = 2.	,	-

1, 2, 2- y = 1, 3-

z = 2.

	,																	:
1		1,1	,	2		1, 2				,	3			2,1		,	4			2, 2		.
1		1,1	,	2		1, 2				,	3			2,1		,	4			2, 2		.

												:
1		1,1	,	2	1, 2			,			3		2,1		,		4		2, 2		.
1		1,1	,	2	1, 2			,			3		2,1		,		4		2, 2		.

	,																						-
.
,				,														2						1, 2	,
,				,														2						1, 2	,

				3			2,1		.									: 1)					x = 1
				3			2,1		.									: 1)					x = 1

2) x = 2.

= 1 2- ( y), 3- ( z).

= 2			:	-
2-	(	y),	3-	( -

z).

= 1, 2 2--

y = 1, 3 3- z = 1.

W (x,, z) = W (1,1,1) =2.

= 2, 3 2--

y = 2, 2 3- z = 2.

W (x,, z) = W (2,2,2) =5.

1--

2/3 1/3,

, ,

: (2)·2/3 + (5)·1/3 = 3.

143

, : = 1

1, 1

1, 2

2,1

2, 2

1,1

W(1,1,1)

W(1,1,2)

W(1,1,1)

W(1,1,2)

1, 2

W(1,1,1)

W(1,1,2)

W(1,1,1)

W(1,1,2)

2,1

W(1,2,1)

W(1,2,2)

W(1,2,1)

W(1,2,2)

2, 2

W(1,2,1)

W(1,2,2)

W(1,2,1)

W(1,2,2)

2	4	2	4
2	4	2	4
1	4	1	;
1	4	1	4
1	4	1	4

= 2

1,1

1, 2

2,1

2, 2

1,1

W(2,1,1)

W(2,2,1)

1, 2

W(2,1,2)

W(2,2,2)

2,1

W(2,1,1)

W(2,2,1)

2, 2

W(2,1,2)

W(2,2,2)

3	3	3	3
0	0	5	5
3	3	3	.
3	3	3	3
0	0	5	5
		144

	1	11	7	5
1	4	8	9	3
	5	5	1	.
3				.
3				11
	2	8	3	13

,	-
:
SA* = [5/11 0 6/11 0]; SB *= [0 0 8/11	3/11].
= 41/33.

[4].

4.9.

			,	-
. 4.10.
. 4.10			,	-
(	),		,	-
(	).			-
	: q1, q2,	, q11;		-
		t 1, t2, ,	t15.
,	tk (k	= 1,.,15),
			W (tk ) :

W (t 1) = 10, W (t 4 ) = 20, W (t 7 ) = -10, W (t 10) = -30, W (t 13) = -30,

W (t2) = -10, W (t5) = 30, W (t8) = 30, W (t11) = 0, W (t14) = 30,

{q2, q3} {q8, q10, q11}.

: {q4, q7} {q5, q6}.

W (t3) = 10, W (t6) = 0, W (t9 ) = 20, W (t12) = 30, W (t15) = 15.

: 1- 3

1 2. , -

1- (1-2 3), - [x1, x2].

145

t15

q11

146

t14

t13

t11

t10

1		2	1	2	1		3	2	1	3	2	1
	q10			q8
	1 3						q6			q5
	2	1
q9	2			1	2	1	1		2		1
q9					2	1	1

	q4				q7
						2
						q3			q2
					0.7	0.2	0.1
					0.7
					3	2	1
						q1

. 4.10

, -

.. ,

1 2 -

. [x1, x2]

x 1, 1-2 1-{q2, q3},

(

), .. x1({q2, q3}) {1,2}.

x2, 3 1- ( {q8,

q10, q11}),					(
					), . .
x2({q8, q10, q11}) {1,2}.
	,	4		:
1	[1,1]	(x1({q2, q3}) = 1, x2({q8, q10, q11}) = 1);
2	[1,2]	(x1({q2, q3}) = 1, x2({q8, q10, q11}) = 2);
3	[2,1]	(x1({q2, q3}) = 2, x2({q8, q10, q11}) = 1);
4	[2,2]	(x1({q2, q3}) = 2, x2({q8, q10, q11}) = 2).
. 4.10		,			:
,				1	-
	2	3 (2-3).	,
			(2-3		1),

[y1, y2].	,		{q4, q7}		-
	1	2.
	,		[y1, y2]		y1, -
			2-3	1-	,
				{q4, q7},
		(
		), . . y1({q4,	q7})	{1,2}.	y2,

1 1- (

{q5, q6}), -

(), .. y2({q5, q6}) {1,2,3}.

,	6	:
1 [1,1]	(y1({q4, q7}) = 1, y2({q5, q6}) = 1);
	147

2	[1,2]	(y1({q4, q7}) = 1,	y2({q5, q6}) = 2);
3	[1,3]	(y1({q4, q7}) = 1,	y2({q5, q6}) = 3);
4	[2,1]	(y1({q4, q7}) = 2,	y2({q5, q6}) = 1);
5	[2,2]	(y1({q4, q7}) = 2,	y2({q5, q6}) = 2);
6	[2,3]	(y1({q4, q7}) = 2,	y2({q5, q6}) = 3).
q 1		1, 2, 3
(		)		0.1,
0.2, 0.7.
			q9,	1
		1/3,	2
2/3.

({Ai, Bj}, q, a),	{Ai, Bj}(i = 1, ,4; j = 1, ,6)	,
	Ai, Bj,	;

q ; .

, {Ai, Bj} q -

, ,

({Ai, Bj}, q, a) = 1; -

, ({Ai, Bj}, q, a) = 0.

, , - 2 [1,2]:

x1({q2, q3}) = 1, x2({q8, q10, q11}) = 2, 6 [2,3]:

y1({q4, q7}) = 2, y2({q5, q6}) = 3.

			{A2, B6}.
:
q1	({A2, B6}, q1, 1)	= 0.1,	p({A2, B6}, q1, 2) = 0.2,
	p({A2, B6}, q1, 3)	= 0.7;
q2	p({A2, B6}, q2, 1) = 1,		({A2, B6}, q2, 2) = 0;
q 3	p({A2, B6}, q3, 1) = 1,		({A2, B6}, q3, 2) = 0;
q 4	p({A2, B6}, q4, 1) = 0,		({A2, B6}, q4, 2) = 1;
q 5	p({A2, B6}, q5, 1) = 0,		p({A2, B6}, q5, 2) = 0,
	({A2, B6}, q5, 3) = 1;
q6	p({A2, B6}, q6, 1) = 0,		({A2, B6}, q6, 2) = 0,
	({A2, B6}, q6, 3) = 1;
	148

q7	p({A2, B6}, q7, 1) = 0,	({A2, B6}, q7, 2) = 1;
q 8	p({A2, B6}, q8, 1) = 0,	({A2, B6}, q8 , 2) = 1;
q 9	p({A2, B6}, q9, l) = 1/3,	({A2, B6}, q9, 2)	= 2/3;
q 10	p({A2, B6}, q10, 1) = 0,	({A2, B6}, q10, 2) = 1;
q 11	p({A2, B6}, q11, 1) = 0,	({A2, B6}, q11, 2)	= 1.
	{A i, Bj}		; tk
,		; q1, , qr	,
	.	({Ai, Bj}, tk)		-
,		tk,		-
	{Ai, Bj}.