. , . : , . .
: , [5.1, .30-73], [5.2].
. . .
. :
L1=R1,
. . . (5.1)
Ln=Rn.
Li Ri, i=1, ... n, , , , , ( ), . . - ( ), . , .
, ,
- , , ( ). . , :
(L1, R1),
. . . (5.2)
(Ln, Rn),
, . , , , , , . .
. , ( ) . , , - . , . . , , , .
5.2.
(. . 5
.1).
/
|
( ) |
x1 |
a[1,1] |
a[1,2] |
... |
a[1,m] |
* |
|
x2 |
a[2,1] |
a[2,2] |
... |
a[2,m] |
* |
|
. . . |
. . . |
xn |
a[n,1] |
a[n,2] |
... |
a[n,m] |
* |
|
s1 |
u[1,1] |
u[1,2] |
... |
u[1,m] |
u[1,m+1] |
|
s2 |
u[2,1] |
u[2,2] |
... |
u[2,m] |
u[1,m+1] |
|
. . . |
. . . |
|
sk |
u[k,1] |
u[k,2] |
... |
u[k,m] |
u[k,m+1] |
|
|
. 5.1. .
, (). . , . (), . , , .. ( *), , , (m+1)-, . , .
, , . (k) , - , () . () (.. u[i, j], i=1, ... m+1, j
=1, ... k) , ( u[i, j]= '+') ( u[i, j]= '- '). , , , . , , . , , , .
. (T
- , T - , T - ). . 0. ( ) , . . 5.2 , . (*) .
|
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|
Ƹ |
Ƹ |
|
|
|
|
T=T |
|
|
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* |
* |
* |
* |
* |
|
T=T |
* |
* |
* |
|
|
* |
* |
* |
|
T>T |
* |
* |
* |
* |
* |
|
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* |
* |
* |
* |
|
|
|
- |
- |
- |
- |
- |
- |
+ |
- |
|
|
- |
+ |
+ |
- |
- |
- |
- |
- |
|
|
- |
- |
- |
- |
+ |
- |
- |
- |
|
T:=0 |
- |
+ |
+ |
- |
+ |
- |
+ |
- |
|
T:=T+1 |
+ |
- |
- |
+ |
- |
+ |
- |
+ |
|
-
- |
- |
- |
- |
+ |
- |
- |
- |
- |
|
|
+ |
+ |
+ |
- |
- |
- |
- |
- |
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- |
- |
- |
- |
- |
+ |
+ |
+ |
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. 5.2. " ".
5.3.
(5.1):
f1(x1, x2, ... , xk)= E1,
. . . . . . . . . . . . . (5.3)
fn(x1, x2, ... , xk)= En,
, ( )
x1, x2, ..., xk,
, , , , .. . . , xj fi (5.3) yj, cij,
y1, y2, , yk
, .
.
s
E
T
() T E s E s T.
fi(x1, x2, ... , xk)= Ei
x1, x2, ... , xk
fi(T1, T2, ... , Tk) Ei ,
T1, T2, ... , Tk
T1, T2, ... , Tk
- ( ) . - .
(5.3) . ()
d1, d2, ... , dk.
, , . .
(
) .
- - , ( , ).
- , - . ( ) .
(2.1) ,
(2.1.1) , , ,
(2.1.2) , .
(2.2) , , .
fi(y1, y2, , yk),
, y1, y2, , yk ( , ).
, .
F(n)=n!. :
F(0)=1,
F(n)=F(n-1)*n.
F(3) .
1- :
F(0)=1, F(3)=F(2) *3.
2- :
F(0)=1, F(3)=F(2) *3, F(2)=F(1) *2.
3- :
F(0)=1, F(3)=F(2) *3, F(2)=F(1) *2, F(1)=F(0) *1.
4- :
F(0)=1, F(3)=F(2) *3, F(2)=F(1)*2, F(1)=1.
5- :
F(0)=1, F(3)=F(2) *3, F(2)=2, F(1)=1.
6- :
F(0)=1, F(3)=3, F(2)=2, F(1)=1.
F(3) 6- .
5.4.
(5.3), , . ( , ) . . [5.3].
, (5.3)
:
X1= phi[1,1] U phi[1,2] U ... U phi[1,k1],
X2= phi[2,1] U phi[2,2] U ... U phi[2,k2],
. . . . . . . . . . . . . . . . . . . . . . . . . . . . (5.4)
Xn= phi[n,1] U phi[n,2] U ... U phi[n,kn],
i- ki=0
Xi=
.
- . , - ( ). A={a1, a2, ... , am} , , (5.4) . X1, X2, ... , Xn , , ( ). phi[i,j], i=1,...,n, j=1,...,kj, :
phi[i,j]
(A U {X1, X2, ... , Xn})* .
phi[i,j] , , . . X1, X2, ... , Xn ,
phi= Z1 Z2 ... Zk , Zi
(A U {X1, X2, ... , Xn}) i=1, ... , k,
Z1, Z2, ... , Zk , aj {aj}. , phi
{p1 p2 ... pk | pj
Zj, j=1, ... , k},
p1 p2 ... pk p1, p2, ... , pk ( ). , (5.4) .
(5.4)
(L1, L2, ... , Ln),
(5.4) X1= L1, X2= L2, ... , Xn= Ln.
(5.4),
X= a X
U b X U X U c
A={a, b, c}.
L={ phi c | phi
{a, b}*}.
(5.4) . L
L1=L U {phi a | phi
{a, b}*}
L2=L U {phi b | phi
{a, b}*}.
(5.4) .
(L1, L2, ... , Ln)
(5.4) ,
(L1', L2',..., Ln')
L1
L1', L2 L2', ... , Ln Ln'.
( , ) L.
(5.3) (5.4) . (5.4) . (5.4)
Ti(X1, X2, ... , Xn).
(5.4)
X1=T1(X1, X2, ... , Xn),
X2=T2(X1, X2, ... , Xn),
. . . . . . . . . . . (5.5)
Xn=Tn(X1, X2, ... , Xn).
(L1[0], ... , Ln[0]) = (
,,...,).
:
(L1[i],...,Ln[i])= (T1(L1[i-1], ... , Ln[i-1]),
. . . . . . . . . . . . .
Tn(L1[i-1], ... , Ln[i-1])).
,
(L1, ... , Ln)
(5.5), ..
(L1, ... , Ln)= (T1(L1, ... , Ln), ... , Tn(L1, ... , Ln))
. T1, T2, ... , Tn.
:
L[0]=
,
L[1]= {c}, L[2]= {c, ac, bc},
L[3]= {c, ac, bc, aac, abc, bac, bbc},
. . . . . . . . . . . . . . . .
L.
-. -
X::= X
X= X
.
5.5.
(5.1) , / .
(5.1) (S, E)
- : S - (5.1) f1, f2, ... , fm ( ) c1,c2, ... , cl, E - , (5.1). , xi, i=1, ... , k, ci, i=1, ... , l, E, - t1, t2, ... , tr, fi, i=1, ... , m, ,
ti1 * ti2 * ... * tik ti0.
, ti=ti', i=1, ... , r, ci=ci', i=1, ... , l. ,
A S,
A
=(t1', ... , tr', f1', ... , fm', c1', ... , cl'),
fi', i=1, ... , m, , fi. , (S, E) ( : ), E, .. E fi', i=1, ... , m, ci', i=1, ... , l, fi
ci .
, , , , . . [5.4], . .
((m, d))=m,
((m, d))=d,
()=,
()=,
, ,
- , - , . D, D1 , , m M, d D, M,
D1, :
: M
M,
: M *
D M,
: M
D1.
, , .
, . : D
- , , D1=D U {}, M - , M={d1, d2, ... , dn | di D, i=1, ... , n, n 0}, ={}, - ( ), D. .
( ), " ". .
5.6.
, , , , . , , .
, . , . : , - (, ), , , . , , . , , ( , ..)
.
- , - .
5
5.1.
function F(x, y: integer): integer;
function G(x, y: integer): integer;
function R(x, y: integer): integer;
:
R(x, y) = x*(y 1),
F(x, y) = R(x + 1, y) - R(x, y - 1),
G(x, y) = F(x, R(x, y)).
G(3, 3).
5.2.
function F(n: integer): integer;
function G(n: integer): integer;
:
F(0)=1,
G(0)=2,
F(n)=G(n-1),
G(n)=F(n-1) + G(n-1).
F(3) G(3).
5.3. E T
{'a', '*', '&', '<', '>'}
E= T U '*' T U E '&' T,
T= 'a' U 'a*' U '<' E '>'
'*a&*a*&a*' ,
'*a&<a&a*>',
'*<*a*&a>&<*a*>*'
E E.
5.4. R .
:
type R= record P1, P2, P3: CHAR end;
function READ(S: R): CHAR; {READ: R CHAR}
function SHIFT(S: R): R; {SHIFT: R R}
function ADD(S: R, C: CHAR): R; {ADD: R * CHAR R}
function REMOVE(S: R): R; {REMOVE: R R}
var X, Y, Z: CHAR;
U: R;
:
SHIFT(ADD(ADD(ADD(U, X), Y), Z)) =
ADD(ADD(ADD(U,Y), Z), X);
REMOVE(U) = SHIFT(ADD(U, '#'));
READ(SHIFT(ADD(U, X))) = X;
:
READ(SHIFT(SHIFT(REMOVE(ADD(ADD(U, 'a'), 'b'))))) =
5.
- .. . : .
- : ( ), 1987.
Ian Sommerville. Software Engineering. - Addison-Wesley Publishing Company, 1992.
. . , / . - .: , 1982. - . 25-53.
. . / . , . , . . . - .: , 1975. - . 98-197.
, , Class - - , , .
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