.
β = δ1γδ2 α = δ1ωδ2 G (VT,VN, P, S ), V = VN VT, δ1, γ, δ2 V*, ω V + , G : ω→ γ P. β α : α =>β. , α β, β α.
β α (: α =>* β), , :
1. β α (α => β);
2. γ, γ α β γ (α =>* γ γ => β).
, α => β, α β, . .
α β , α =>+ β. , . , α =>3 β , β α .
, β, , . , , , , .
L, G (VT, VN, P, S ) G. L, G L(G). L(G) VT, VT. , , , . ( , ).
, . , , .
: S => Y => TY => TT => YTT => TTT, S => T => TX => T5 => T6. F => R - .
, , , TFT => TFFT => TFFF => FFFF => FFTFF.
|
|
2 3 (- ) . , .
G (VT,VN, P, S ), , :
VN VT;
, S;
, ,
A VN, b, b2... bn; n > 0, 0 < i < n, bi (VN VT { }), G (VT,VN, P, S ), → b1b2bn .
, 2 3 (- ). ( ).
, . : . : , .
, . , . ( , ) , , , . , , .
. , () . , ( ). , . . , ( ), .
, ( , ). , , , .
|
|
, , , ( ) . , , , . .
G ({+, , *, /, (,), x, y}, {S}, P, S):
P: S → S+S | SS | S*S | S/S | (S) | x | y
: , , , .
, , x*y+x :
S => S+S => S*S+S => x*S+S => x*y+S => x*y+x
S => S*S => x*S => x*S+S => x*y+S => x*y+S
(. 1).
. 1. x*y+x
( ) . , , , . . , . .
, . , :
G ({+, , *, /, (,), x, y}, {S, , }, P, S):
P: S → S+T | ST | T
T→ T*E | T/E | E
E→ (S) | x | y
x*y+x :
S => S+T => T+T => T*E+T => E*E+T => x*E+T => x*y+T => x*y+E => x*y+x
. 2 .
. 2. x*y+x
, , , . , , . . , - , G (VT, VN, P, S ) , . :
1) → | α
2) → α | β
3) → α | β | γ
4) → α | αβ | γ
A VN; α, β, γ (VN VT)*.
- , , . , , . , .
, . - . , , , .
1. ?
2. ?
|
|
3. ?
4. .
5. ?
6. :
) ;
) , ;
) ;
) .
1. G ({ , i, f, t, h, e, n, l, s, b, a }, {E}, P, E ) :
P: E → if b then E else E; | if b then E; | a
, , . , .
2. .
3. :
3.1) G1 ({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, , .}, {<>, <>, <>, <>, <>, <>}, P1, <>)
P1:
<> → <> <>
<> → | + | -
<> → <>. <> | <>.
<> → <> | <> <>
<> → | <>
<> <> → <> <> <>
<> → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7| 8 | 9
3.2) G2 ({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, , .}, {<>, <>, <>, <>}, P2, <>)
2:
<> → +<>| -<> | <>
<> → <>.<> |<>. |<>
<> → <> | <> <>
<> <> → <> <> <>
<> → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7| 8 | 9
3.3) G3 ({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, , .}, {<>, <>, <>}, P3, <>)
3:
<> → +<>| -<> | <>
<> → <>. | <> | <>0 | <>1 | <>2 | <>3 | <>4 | <>5 | <>6 | <>7| <>8 | <>9
<> → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7| 8 | 9 | <>0 | <>1 | <>2 | <>3 | <>4 | <>5 | <>6 | <>7| <>8 | <>9
4. , 3.
5. -57, 196, 11.9 3.
6. , 3 , :.124,.34.