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Kursova robota (4)

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? ?????????? "????????? ?????? ???????? ?????????"
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????? ??-22, ???????? ?????? ? 2230
???????? ?? ???????__________________
????? ?????????? ???????? - 100010110110
_______________________
(?????? ?????????) ???? - 2012?.
???? ??????? ? ??????????????????????????????????????????????????12???????????? ????????34?????????? ??????56?4????.109118.002 ?? ???????? ????????57?3????.109118.003 ?2 ???????? ???????1 8 ????? ??????????9 ?????????????10?4????.109118.004 ?? ???????????? ???????19
???????? ????????
?????
1. ??????????? ?????????????? ??'???? 2
2. ?????? ???? ??? ???????? 2
3. ????? ????????? 4
4. ????? ? ??????? ???????????? _______________________4
5. ??????? ????????? ? ????????? ???????????? 4
1 ??????????? ?????????????? ??'???? ? ???????? ?????? ????????? ???????? ?????? ???????? ????. ???????? ??????? - ?? ?????, ?? ??????? ???????????? ???????? ??????? ? ???????? ?? ??????? ??????????. ????????? ???????????? ?????? ???????? ??????? ? ??????? ?????????????? ???????.
2 ?????? ????
??????? ???????? ???????????? ???'????? ????????? ????????? ????????? ?????? ????????????? ? ????????? ??????? ????????.
h9h8h7h6h5h4h3h2h1010110110
??????? ?'??????? ?????????( h8 h4 h2 =101):
3,2,4.
??????? ?????( h8 h7 h3 = 101):
not X2, not X2, not X1.
????????????? ???????? ????????( h9 h4 h1 = 000): (Y1 Y2), Y3, (Y4 Y5), Y2, Y3, (Y1 Y3). ?????? ?????????? 2t(h6 h2 = 11):
Y4.
??????( h6 h5 = 11):
T - ??????.
??????? ????????( h3 h2 h1 = 110):
3 ???-??, 3?.
??? ????????( h4 = 0):
????????? ??????? ???? .
????????? ????-????? ????????? ???????????? ?? ??????? 2.1.
??????? 2.1- ????????? ????-????? ?????????
??????? ? ???????? ????????????? ??????? ?????? ???????? 2.1:
x4x3x2x1f1f2f3f4000011100001110100101111001100000100-0100101000101101--00111--111000100010010011101000011011000111001-11110111001110110011111111
??????? 2.1 - ??????? ?????????? ??????? ???????
????????? ???????? ??????? ??????????? ??????? f1, f2, f3. ???????? ?????????? ????????????? ??? ?????????? ??????? ??????? ?? ??????????????? ???????? ????????.
??????? f4 ????????? ??????????? ? ?????????? ?????? ??????? ????, ?????????, ????? ?? ???????. ????????? ?????????? ????? ??????? ?? ?'??? ??????????? ??????. ???????? ??????????? ??????? ????????:
- ???????????? ????????????;
- ?????? (??????-???-??????);
- ??????? ?????. 3 ????? ?????????
???????? ???????.
???????? ??????? ??????????? ? ????????????? ????? ? ???'??? ?? ????????. ??? ???????? ? ?????????? ????? ?????? ? ?????????? ????????.
?????????????? ??????? ???????.
??? ??????????? ?? ???? (???'???????? ? ???'????????? ) ???????, ?? ?????? ?????? ???????????? ?? ????? ?????? ? ?????????? ??????????? ???????????? ????? ? ?????? {?/???, ?/???-??}.
4 ????? ???????????? ? ??????? ?? ?????????
1) ???????? ?????? ????????
2) ?????????? ???????? ?? ????????? ?????????
3) ???????? ????? ????????
4) ???????? ??????? ?????????
5) ???????? ??????????? ??????? ????????
6) ?????? ????????????? ???? ??? ??????? ????????? ???????? ? ???????? ????????
7) ???????? ????? ???????? ? ???????? ??????. 5 ??????? ????????? ? ????????? ????????????
????????? ????
????? ? ??????? "???? ???????"
???? ???????
????? ? ??????? "???????? ????????"
???????? ????????
????? ? ??????? "???????? ???????. ????? ?????????? ?????????????"
???????? ???????. ????? ?????????? ?????????????
????? ? ??????? "???????????? ???????"
???????????? ???????
???????? ??????? ????? ?????????? ?????????????
???????????? ???????
?????
1 ????? 2
2 ?????? ???????? 2
2.1 ??????????? ?????? ????????____________________________________ 2
3 ?????? ????????????? ???? 7
3.1 ?????_______________________________________ 7 3.2 ????????????? ??????? f4 ? ?????????? ????? ??????? ????______________ 7
3.3 ????????????? ??????? f4 ? ?????????? ????? ??????? ?????????_________ 7
3.4 ????????????? ??????? f4 ? ?????????? ????? ??????? ?????_____________ 7
3.5 ????????????? ??????? f4 ? ?????????? ????? ??????? ???????_________ 8
3.6 ?????????? ?????????? ??????? f4 ?? ?'??? ??????? ??????____________ 8 3.7 ??????????? ??????? f4 ??????? ???????????? ????????????______________ 8
3.8 ??????????? ??????? f4 ??????? ??????-???-??????____________________ 9
3.9 ??????????? ??????? f4 ??????? ??????? ?????_________________________10
3.10 ??????????? ??????????? ??????? f4 ??????? ???????????? ????????????__10
3.11 ??????????? ??????????? ??????? f4 ??????? ??????-???-??????________11
3.12 ??????????? ??????????? ??????? f4 ??????? ??????? ?????_____________12
3.13 ???????????? ????? ?????????? ??????? F4___________________________________________13
3.14 ??????? ??????????? ??????? f1, f2, f3 13
3.15 ????????? ??????????? ???? ??? ?????????? ?? ??? 16
4 ???????? 18
5 ?????? ?????????? 19
1 ?????
? ????? ???????? ?????? ????????? ???????? ?????? ???????? ? ?????? ????????????? ????. ???????? ??????????? ?? ???????? "?????????? ???????? ????.109118.002 ??".
2 ?????? ????????
2.1 ??????????? ??????
?? ????????? ?????? ????????? (??????? 2.1 "?????????? ???????? ????. 109118.002 ??") ????????? ???????? ?????? ???????? (??????? 2.1.1): ??????? 2.1.1 - ???????? ?????? ???????? ???? ?????? ? ??? ( ??????? 2.1.1) ????????? ???? ???????? ???? (???. 2.1.2), ????????? ????????? ?????? ????????.
??????? 2.1.2 - ???? ????????
??? ??????? ???????? ????? ???????? ????????? ???????? ?????? ??????? ????????? ???????? ?? ???????? ??????? ????????. ????????? ?????? ???????? ???????? 5, ????????? ???????? ???????? ?? ???????? K>= ]log2N[ = ]log25[ = 3, ?????? ? = 3. ??? ?? ??? ???????? ?????? ???????? ????????? ??????????????? T-???????, ???????? ??????? ????????? ????? ???? ???????? (??????? 2.1.3).
??????? 2.1.3 - ??????? ????????? T-???????
?? ?????? ????? ???????? (??????? 2.1.2) ???????? ?????????? ??????? ???????? (??????? 2.1.1).
??????? 2.1.1 - ?????????? ???????
???????? ??????????? ?????????? ?????????????? ?????????????? ?????????? ?????????X1X2Y1Y2Y3Y4Y5T3T2T1Z1000Z2001000100001Z1000Z2001--111000001Z2001Z3011----00011010Z3011Z4111----00010100Z4111Z5101--100000010Z4111Z5101--001000010Z5101Z51010--00100000Z5101Z10001--10100101 ?? ?????? ??????????? ??????? ???????? (??????? 2.1.1) ????????? ?????? ????????????? ???? ??? ???????? ???????? ? ??????? ????????? ????????. ??????????? ??????? ????????? ???????? ?? ???????? ???????? ? ???? ?????? ?? ?????? ???????. ????????? ??????????? ??????????? ???????????? ??????? ??????? ??????? ????? (??????? 2.1.4, 2.1.5). ?????????, ?? ????????? ??????????? ??????????, ?? ?????????? ????? ?/???-?? ??????????? ?? ??????????? ???????. ?????????? ????????????? ??????? ?????????? ?????????? ?????????? ????? {3 ???-??, 3?}. ??????????? ??????? ??????? ??????? ????? (??????? 2.1.4)
????? ??????????? ??????? ???? ?????? ? ???????? ??????????? ??????. ??????? ????? ??????????? ???????? ???????? ????????.
?????? ????????? ????? 2 ???????: ???????? ?????? ?? ???? ???????????. ???? ??? ????????? ????????????? ?????, ????? ??????????????? ??????????? ????????? ??????? ???????,??? ??????? ???????? ?? ?????? ???????? ??????.
????? ?????? ???????? ???????? ?????? ? ?????? ???????? ???????????????? ???????????? (????) ? ???????? ? ????????? "???????? ???????. ????? ?????????? ????????????? ????.109118.003 ?2".
3 ?????? ????????????? ????
3.1 ?????
????? ???????? ?????? ??????? ????????????? ??????? f4 ? ?????????? ?????? ??????? ????, ?????????, ????? ? ???????.
3.2 ????????????? ??????? f4 ? ?????????? ????? ??????? ????.
? ????? ??????? ????????? ??????? {?, ???, ??}.
f_(4 ????)=(x_4 x_3 x_2 ) �x_1 ? (x_4 x_3 ) �x_2 (x_1 ) � ? (x_4 ) �x_3 (x_2 ) �x_1 ?( x_4 ) �x_3 x_2 x_1 ? x_4 (x_3 x_2 ) �x_1 ? x_4 (x_3 ) �x_2 (x_1 ) � ?
? x_4 (x_3 ) �x_2 x_1 ? x_4 x_3 (x_2 ) �x_1 ? x_4 x_3 x_2 x_1 f_(4 ????)=(x_4 ? x_(3 )? x_2 ? x_1 )�(x_4 ? x_(3 )? (x_2 ) � ? (x_1 ) � )�(x_4 ? (x_(3 ) ) �? x_2 ? x_1 )
(x_4 ? (x_(3 ) ) �? (x_2 ) � ? x_1)�((x_4 ) � ? x_(3 )? x_2 ? x_1)�((x_4 ) � ? (x_(3 ) ) �? x_2 ? (x_1 ) �)�((x_4 ) � ? (x_(3 ) ) �? (x_2 ) �? x_1)
??? ????????? ?????? ??????? ??????? ??????? ???????????? ?????? ????? ??????????? ?????????? ?????? ???????.
f_(4 ????)=1 ? 2 ? 5 ? 7 ? 9 ? 10 ? 11 ? 12 ? 15
f_(4 ????)=0 ��3 ��4 ��6 ��8 ��(13) ��(14) �
3.3 ????????????? ??????? f4 ? ?????????? ????? ??????? ?????????.
? ????? ??????? ????????? ??????? {?, ???????? ???, const 1}.
f_4=(?(x?_4?1)(x_3?1)(x_2?1)x_1)?(?(x?_4?1)(x_3?1)x_2 (x_1?1))?
(?(x?_4?1)x_3 (x_2?1)x_1)? (?(x?_4?1)x_3 x_2 x_1)?(x_4 (x_3?1)(x_2?1)x_1)?
(x_4 (x_3?1)x_2 (x_1?1))?(x_4 (x_3?1)x_2 x_1)?(x_4 x_3 (x_2?1)(x_1?1))?
??(x?_4 x_3 x_2 x_1)=x_4 x_3 x_2 x_1?x_4 x_3 x_2?x_4 x_2 x_1?x_4 x_3?x_3 x_2?x_2?x_1
3.4 ????????????? ??????? f4 ? ?????????? ????? ??????? ?????.
? ????? ??????? ????????? ??????? {???-??}.
f_4=((x_4 ? x_(3 )? x_2 ? x_1 )�(x_4 ? x_(3 )? (x_2 ) � ? (x_1 ) � )�(x_4 ? (x_(3 ) ) �? x_2 ? x_1 ) ) � �
((x_4 ? (x_(3 ) ) �? (x_2 ) � ? x_1 )�((x_4 ) � ? x_(3 )? x_2 ? x_1 )�((x_4 ) � ? (x_(3 ) ) �? x_2 ? (x_1 ) � )�((x_4 ) � ? (x_(3 ) ) �? (x_2 ) �? x_1 ) ) � �=
(x_4?x_3?x_2?x_1)?(x_4?x_3??(x?_2 ??x?_2)?(x_1?x_1))?(x_4?(x_3?x_3)?x_2?x_1)
(x_4?(x_3?x_3)?(x_2?x_2)?x_1)?(?(x?_4?x_4)?x_3?x_2?x_1)?
?(?(x?_4 ??x?_4)?(x_3?x_3)?x_2?(x_1?x_1))?(?(x?_4 ??x?_4)?(x_3?x_3)?(x_2?x_2)?x_1)
3.5 ????????????? ??????? f4 ? ?????????? ????? ??????? ???????
? ????? ??????? ????????? ??????? {?-??}.
f_4=(((x_4 x_3 x_2 ) �x_1 ? (x_4 x_3 ) �x_2 (x_1 ) � ? (x_4 ) �x_3 (x_2 ) �x_1 ?( x_4 ) �x_3 x_2 x_1 ? x_4 (x_3 x_2 ) �x_1 ? x_4 (x_3 ) �x_2 (x_1 ) � ) �?) �
(?( x_4 (x_3 ) �x_2 x_1 ? x_4 x_3 (x_2 ) �x_1 ? x_4 x_3 x_2 x_1 ) � ) �=((x_4/x_4)/(x_3/x_3)/(x_2/x_2)/x_1)/
((x_4/x_4)/(x_3/x_3)/x_2/x_1) / ((x_4/x_4)/x_3/(x_2/x_2)/x_1)/((x_4/x_4)/x_3/x_2/x_1)/
(x_4/(x_3/x_3)/(x_2/x_2)/x_1)/(x_4/(x_3/x_3)/x_2/(x_1/x_1))/(x_4/(x_3/x_3)/x_2/x_1)/
(x_4/x_3/(x_2/x_2)/(x_1/x_1))/(x_4/x_3/x_2/x_1)
3.6 ?????????? ?????????? ??????? f4 ?? ?'??? ??????? ??????
1. ???? ??????? ???????? ????, ??? ?? F(0000)=0.
2. ???? ??????? ???????? ???????, ??? ?? F(1111)=1.
3. ???? ??????? ?? ???????????, ??? ?? F(0101)=1, F(1010)=1.
4. ???? ??????? ?? ?????????, ??? ?? F(0010)> F(0011).
5. ???? ????? ?????????, ??? ?? ????????? ????? ??????? ?????????, ?? ???????? ? ?????????? 3.3 ? ?? ???????? ?????????.
?? ?????? ????????????? ?????? ????????, ?? ??????? f4 ???????? ?????? ???? ? ?? ???????? ???????? ????? ??????????? ??????.
?? ???????? ?????-??????????? ????????, ?? ???? ??????? ?? ? ????????????? ??????.
3.7 ??????????? ??????? f4 ??????? ???????????? ???????????? ???? ????? ?????? ??????? ? ?????????? ?????????? ???????????? ??? ?????? ??????????. ???????? ??? ??????????? ???????????? ??????????? ???????? (??????? 3.7.1). ????????? ??????????? ??? ?????? ?? ???? ??????? ??????? ??????? ????????. ?????????? ??? ???????? ??????? ??????????? ? ??? ?????? ???????, ?? ?????????? ????? ????????? ?????????? ???; ?????????? ?? ??????????, ?? ??????????? ? ????? ??? ???.
???? ??????? ???????????? ?????????????? ?? ??????? ???????? ???????
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
????????? ???? ???????:
f_4= x_4 x_3 (x_2 x_1 ) �? (x_3 ) �x_2 (x_1 ) �? x_3 x_2 x_1? (x_4 x_2 ) �x_1? x_4 (x_3 ) �x_1
3.8 ??????????? ??????? f4 ??????? ??????-???-??????
???????? ? ??????? ?????????? ???????, ???????? ???????? ???? (?0).
1) ?????'??? ?? ?? ????? ?? ????????? ??????????.
2) ?????'??? ????? ????? ?? ????????? ?????????? ?? ????? ?? ????????? ??????? ? ?????.
3) ????????? ??????? ?????????? ??? ???????, ??? ??????? ?? ?????? ????? ?? ?????????? ?? ? ???? ????????? ??????? ????????????? ?? 1. 4) ?????? ??????????
5) ?????????? ?????? 1-4 ???? ???????, ????? ????? ??????? ??????? ???????? ? ????????? ????.
K_0={�((�(0001@0010)�@(�(0101@1001@1010@1100)�@(�(0111@1011)�@(1111� )� K_1={�({�((�(x001@x010)�@(x111� )�@{�((0x01�@(1x11� )�@{(�(01x1@10x1)��@{101x� )�
????????? ?????????? ?????? (???. 3.8.1).
???????????? ?????????? ?? ???????, ???? ??????? ??????? ????????:
??????? 3.8.1-??????? ???????? ???????
??????????0001001001010111100110101011110011111100+x001++x010++x111++0x01++1x11++01x1++10x1++101x++
???? = {1100; x010} ????=1100 ? x010 ? x111 ? 0x01 ? 10x1
????: f_4= x_4 x_3 (x_2 x_1 ) �? (x_3 ) �x_2 (x_1 ) �? x_3 x_2 x_1? (x_4 x_2 ) �x_1? x_4 (x_3 ) �x_1
3.9 ??????????? ??????? f4 ??????? ??????? ?????
????????? ??????????? ??????? ??????? ????? (???. 3.9.1). ??? ????? ???? ??????? ??? ??????????? ??????? ? ????????? ????????? ??????????. ????? ???????? ?????????? ????????????, ? ??????????? ? ??????? ???????? - ??????????.
??????????? ???? ???? ?????? ??????????? ? ????????? ????????,?? ???????? 2k ,k ? N.
X3 X41010 0111X2 0101 0110 X1 ??????? 3.9.1 - ??????????? ??????? ??????? ??????? ?????
f_4= x_4 x_3 (x_2 x_1 ) �? (x_3 ) �x_2 (x_1 ) �? x_3 x_2 x_1? (x_4 x_2 ) �x_1? x_4 (x_3 ) �x_1
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