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827 0688759652

:

- . , , " " " ", .

2963-2 (RUS) . :

2963-2

II ... 372:

!

.

.

, . , , , - D. D. , MAX+PLUSII, , , , 23 , - 1020 .

[1] 50 , 9 (C, D, CI, DI, DO, DIO, CI, DI, DIO) . : D. D Ը (CI, DI), (DO), (DIO), ݸ (CI, DI), ݸ (DIO).

, D. , , D , .

D ( ) ( ). . .

, . , . , N intlog2M, M - , . , : ( , ). .

L X = {x1,...,xL}, N Y = {y1,...,yN}, M A = {a1,...,aM}, R ( ) D = {d1,...,dR} E = {e1,...,eR}.

R , dN+1,...,dN+R, ޸ eN+1,...,eN+R. , . , ( [2]) , , [2] E = {e1,...,eN+R}.

1

( ).

  1. ai, ai € A, , . W. , - . , W ̸ . i j , yj € Y(ai), Y(ai) - , ai, ai € A. W, ai, W(ai), ai € A.
  2. .

    2.1. W W1,...,WH, , W(ai) € Wh W(aj) € Wh, W(ai) = W(aj), h = ¯1,H.

    2.2. R dN+1,...,dN+R, R = intlog2 (max(|W1|,...,|WH|)). W R .

    2.3. Wh, h = ¯1,H R, dN+1,...,dN+R. W(ai), |C(ai)| = max, C(ai) - , ai, ai “ A.

  3. Ը W ̸ , y1,...,yN, , dN+1,...,dN+R. . W ̸ .

    , W(a1), , .

  4. . ai, ai € A, . j W(ai) , ei ϸ , , - , ̸ , ei .
  5. .

d1,...,dN+R , ޸ d1,...,dN , dN+1,...,dN+R , ( ) . , d1,...,dN, e1,...,eN, y1,...,yN. , . , dN+1,...,dN+R, eN+1,...,eN+R.

1. 1 , . 1. W . 2 ( W ""). W , W1 = {W(a1), W(a6)}, W2 = {W(a3), W(a5)} W3 = {W(a4), W(a7)}. W1,...,W3 , d6 W1,...,W3. , W(a3) W(a7), |C(a3)| > |C(a5)| |C(a7)| > |C(a4)|. 3 W . W . 3. , e1,...,e6. ̸ W :

K(a1) = ¯e1·¯e3·¯e4·¯e6;
K(a2) = e1·e2;
K(a3) = ¯e1·e2·e3·¯e4·¯e6;
K(a4) = ¯e1·¯e2·e4·e5·e6;
K(a5) = ¯e1·e2·e3·¯e4·e6;
K(a6) = ¯e1·¯e3·¯e4·e6;
K(a7) = ¯e1·e4·e5·¯e6;
K(a8) = ¯e1·e4·¯e5.

. 4. :

d1 = ¯e1·¯e3·¯e4·¯e6;
d2 = ¯e1·¯e3·¯e4·¯e6 + e1·e2·¯x1 + ¯e1·¯e3·e4·e5·e6 + ¯e1·e4·e5·¯e6·¯x5;
d3 = ¯e1·e2·¯x1 + ¯e1·¯e2·e4·e5·e6 + ¯e1·e4·e5·¯e6·¯x5;
d4 = ¯e1·e2·e3·¯e4·¯e6 + ¯e1·¯e3·¯e4·e6·x4 + ¯e1·e4·e5·¯e6·x5;
d5 = ¯e1·e2·e3·¯e4·¯e6 + ¯e1·¯e3·¯e4·e6·x4;
d6 = e1·e2·x1 + ¯e1·e2·e3·¯e4·¯e6·x2 + + ¯e1·¯e2·e4·e5·e6·x3 + ¯e1·¯e3·¯e4·e6·¯x4 + + ¯e1·e4·e5·¯e6·¯x5·x3.

1.

am X(am, as) as Y(am)
a1 1 a2  
a2 x1
¯x1
a6
a3
y1, y2
a3 x2
¯x2
a4
a7
y2, y3
a4 x3
¯x3
a5
a3
y4, y5
a5 1 a1 y2, y3
a6 x4
¯x4
a7
a6
a7 x5
¯x5 x3
¯x5 ¯x3
a8
a5
a3
y4, y5
a8 1 a1 y4

2. W

ai / yj y1 y2 y3 y4 y5
a1 - - - - -
a2 1 1 - - -
a3 - 1 1 - -
a4 - - - 1 1
a5 - 1 1 - -
a6 - - - - -
a7 - - - 1 1
a8 - - - 1 -

3. W


ai / yj y1 y2 y3 y4 y5 d6
a1 0 - 0 0 0
a2 1 1 - - - -
a3 0 1 1 0 - 0
a4 0 0 - 1 1 1
a5 0 1 1 0 - 1
a6 0 - 0 0 - 1
a7 0 - - 1 1 0
a8 0 - - 1 0 -

4.

am K(am) X(am, as) as K(as) Y(am) D(am, as)
a1 ¯e1·¯e3·¯e4·¯e6 1 a2 e1·e2 - d1,d2
a2 e1·e2 x1
¯x1
a6
a3
¯e1·¯e3·¯e4·e6
¯e1·e2·e3·¯e4·¯e6
y1, y2 d6
d2,d3
a3 ¯e1·e2·e3·¯e4·¯e6 x2
¯x2
a4
a7
¯e1·¯e2·e4·e5·e6
¯e1·e4·e5·¯e6
y2, y3 d4,d5,d6
d4,d5
a4 ¯e1·¯e2·e4·e5·e6 x3
¯x3
a5
a3
¯e1·e2·e3·¯e4·e6
¯e1·e2·e3·¯e4·¯e6
y4, y5 d2,d3,d6
d2,d3
a5 ¯e1·e2·e3·¯e4·e6 1 a1 ¯e1·¯e3·¯e4·¯e6 y2, y3 -
a6 ¯e1·¯e3·¯e4·e6 x4
¯x4
a7
a6
¯e1·e4·e5·¯e6
¯e1·¯e3·¯e4·e,sub>6
- d4,d5
d6
a7 ¯e1·e4·e5·¯e6 x5
¯x5 x3
¯x5 ¯x3
a8
a5
a3
¯e1·e4·¯e5
¯e1·e2·e3·¯e4·e6
¯e1·e2·e3·¯e4·¯e6
y4, y5 d4
d2,d3,d6
d2,d3
a8 ¯e1·e4·¯e5 1 a1 ¯e1·¯e3·¯e4·¯e6 y4 -

. , , .

   .

, . , . Ը . ( [3]) , . .

(am) - , am, am € A. , am, am € A, :

Y(am,ah) = Y(am,at), (1)
ah,at € A(am), h t, Y(am,as) - , am as, Y(am,as) Y, am,as € A.

, .

P(am) - am, am € A; Pk(am) - am, Pk(am) P(am); Yk(am) - , Pk(am), Yk(am) Y, ޸ Pk(am). .

2

  1. am, am € A, (1), 5.
  2. am, am € A, (1). P1(am),...,PK(am) am, Y1(am),...,YK(am), , Yk(am) Yh(am) k h, k,h = ¯1,K.
  3. am, 3.

    3.1. K aM+1,...,aM+K.

    3.2. P(aM+1),...,P(aM+K) aM+1,...,aM+K, P(aM+k) := Pk(am), k = ¯1,K.

    3.3. C(aM+1),...,C(aM+K) aM+1,...,aM+K, (aM+k):= (am), k = ¯1,K.

    3.4. A := A\{am} A := A {aM+1,...,aM+K}.

    3.5. .

  4. 1.
  5. .

D

D , ( ). D , : , , , .

B(as) - , as, as € A. D "" , as, as € A, :

Y(ah,as) = Y(at,as), (2)
ah,at € B(as), h t

as, as € A, . D .

k(as) , as, k(as) (as); Zk(as) - , Ck(as), Zk(as) Y, ޸ Ck(as). A D, (2), .

3

  1. A (2), 5.
  2. as, as € A, (2). C1(as),...,CK(as) as, Z1(as),...,ZK(as), , Zk(as) Zh(as) k h, k,h = ¯1,K.
  3. as, 2.

    3.1. K aM+1,...,aM+K.

    3.2. P(aM+1),...,P(aM+K) aM+1,...,aM+K, P(aM+K) := P(as), k = ¯1,K.

    3.3. C(aM+1),...,C(aM+K) aM+1,...,aM+K, C(aM+K) := := k(as), k = ¯1,K.

    3.4. A := A\{as} A := A {aM+1,...,aM+K}.

    3.5. .

  4. 4. 1.
  5. 5. .

, D . D .

4

  1. ai, ai € A, , . W. , - . , W ̸ . i j W , am € B(ai), yj € Y(am,ai).
  2. 24 1.
  3. .

3 4 D [4].

D

D ZUBR, :

  1. .
  2. (1), 1; D (2), 3.
  3. : 1, D 4.
  4. , .
  5. 4 .

ZUBR :

  • / ;
  • ;
  • (, );
  • .

. ZUBR : VHDL, Verilog, AHDL, Abel .

D

, MCNC (Microelectronics Center of North Carolina) [5]. MAX+PLUSII Altera.

MAX+PLUSII CLASSIC (q = 8, q - , ) MAX 5000 (q = 4). . 5, Name - ; L N - , ; CA1 CA2 - MAX+PLUSII CLASSIC MAX 5000, ; CC1 CC2 - q = 8 q = 4, ; Type - .

5.

Name L N CAL CCL CAL/CCL CA2 CC2 CA2/CC2 Type
bbsse 7 7 41 19 2,16 22 19 1,16 A
beecount 3 4 8 6 1,33 8 6 1,33 A
dk16 2 3 - - - 33 14 2,36 A
dk17 2 3 11 9 1,22 12 6 2 A
donfile 2 1 - - - 17 1 17 C
ex4 6 9 15 12 1,25 14 12 1,17 ~B
mark1 5 16 35 20 1,75 - - - A
mc 3 5 8 5 1,6 8 5 1,6 C
s386 7 7 49 20 2,45 22 20 1,1 A
s8 4 1 - - - 4 1 4 C
shiftreg 1 1 4 3 1,33 4 2 2 B
  13,09   31,23  
mid   1,64   3,12  

. 5 , ĸ CLASSIC, , 1,64 ( - 2,45 ), MAX 5000, , 3,12 ( - 17 ).

, D MAX+PLUSII MAX 9000 (q = 4) FLEX 10K (q = 5). , MAX 9000 FLEX 10K ( ) . . 6, CA3 CA4 - MAX+PLUSII MAX 9000 FLEX 10K, ; CC1 CC2 - D q = 4 q = 5, .

6. D

Name L N CA3 CDI CA3/CDI CA4 CD2 CA4/CD2 Type
beecount 3 4 9 6 1,5 36 10 3,6 A
ex4 6 9 13 13 1 29 14 2,07 ~B
keyb 7 2 31 16 1,94 103 20 5,15 ~D
lion9 2 1 6 4 1,5 24 4 6 A
opus 5 6 10 7 1,43 27 8 3,38 ~D
s1 8 6 52 14 3,71 141 15 9,8 D
s27 4 1 4 4 1 43 4 10,75 D
s386 7 7 16 16 1 59 20 2,95 A
s8 4 1 5 1 5 23 1 23 C
train11 2 1 7 3 2,33 25 3 8,33 A
  20,41   75,03  
mid   2,04   7,50  

. 6 , ĸ D MAX 9000, , 2,04 ( - 5 ), FLEX 10K, , 7,5 ( - 23 ).

, D 23 , .

  1. D .
  2. C D, A B, ޸ , , , .
  3. D , , , A B.
  4. C D, A B, , , , , .
  5. , (, MAX+PLUSII Altera), , ĸ .
  6. , D .
  7. , D - .
  8. , D - , , .
  9. D , ( (1)) D ( (2)).
  10. D ( s8 . 6).
  11. D , FPGA ( FLEX 10K).
  12. D .

D.

( , D ) 3 1, Ը .

D , .

, , , yi ¯yi, , - Q(yi) Q(¯yi), Q(yi) - , yi, yi € Y.

Ը .

  1. .. // Chip News. 9. . 414.
  2. .. . .: , 1981. 416 .
  3. .. . .: , 1962. 476 .
  4. .. . .: - , 2001. 636 .
  5. Yang S. Logic synthesis and optimization benchmarks user guide. Version 3.0. Technical Report, Microelectronics Centre of North Carolina, 1991. 43 p.







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