Truong hQpbai roan H~G la kh6ng giai duQcthl ta noi gia thie'tH thie'u.

D, w) Voi m6i lu~ tr mftta co th€ ap d1,lngtre nH de suy ra nhung thuQctinh

Truong hQpbai roan H~G la kh6ng giai duQcthl ta noi gia thie'tH thie'u.

Khi do co th§ di€u chinh bai roan b~ng nhi€u cach khac nhau d§ cho bai roan la giai duQc. Ch~ng h~n ta co th€ sa dl:lngmQt s6 phuong an sail day:

phu'dngan 1 : TIm mQtA' c M \ (A u B) t6i ti§u saG cho baa dong cua t~p

hQpA'u A chlia B.

phu'dngan 2 : Khi phuong an 1 kh6ng th§ tht;tchi~n duQc thl ta kh6ng th§ chI

di€u chinh gia thie't el§cho bai roan la giai duQc. Trang tint hu6ng n~y, ta phai bo bot ke't lu~n ho~c chuy€n bot mQt ph~n ke't lu~n sang gia thie't d§ xem xet l~i bai roan rhea phuong an 1.

Khai ni~m t~p hQp sinh va phuong phap Hm mQt t~p hQp sinh tren mQt m~ng suy

di~n la co sd cho vi~c phat tri§n cac thu~t roan giai quye't va'n d€ ki§m dint gia

thie't cua bai roan suy di~n. Hon lllIa vi~c khao sat v€ t~p hQp sinh cling Ia n1Qt va'n d€ duQc d~t ra mQt each tt;tnhien tren m~ng suy di~n nh~m tim fa mQt t~p hQp t6i thi§u cac thuQc tint va cac lu~t suy di~n sinh fa ta't ca cae thuQc tint khac.

'I

2.5.1 Khai ni~m t~p hQ'psinh

- Dinh nghla 2.7: Cho (A, D) la mQt m~ng suy di~n. MQt t~p thuQc tint SeA

duQc gQi la mQt tqp ht;Jpsinh cua m~ng suy di~n khi ta co baa dong cua S tren m~ng la A, nghia la S

=

Vi du 2.13: Xet m~ng suy di~n (A, D) voi A

=

bie'n s6tht;tc duong va D la t~p hQp cac lu~t suy di~n tuong ling cua cac quail

h~ suy di~n th§ hi~n bdi cac c6ng thlic sail day:

f1:A+B+C=n f2: a/sin(A)

=

=

=

=

=

=

=

=

M(;mg suy di~n nfiy co mQt t~p hqp sinh la T= {a, A, B} va tu T ta suy ra duqc D

nho cac lu~t suy di~n sail:

A, a ::::>R; A, B ::::>C; R, C ::::>c; R, B ::::>b; a, b, c ::::>p; a, b, c, p ::::>S

Tli dinh nghla v~ t~p hqp sinh (j tren ta co cac tinh chit sail:

(1) Ne'u S Ia mQt t~p hqp sinh trong mQt m~ng suy di~n va SeT thi T cfing la mQtt~p hqp sinh.

(2) Ne'u S Ia mQt t~p h<;1psinh trong m~ng suy di~n (A, D) va D' la mQt t~p hqp mC1rQng cua D, nghla la D cD', thi ta cling co S la mQt t~p h<;1psinh cua m?ng suy di~n (A, D').

Hi6n nhien la m6i m~ng suy di~n d~u co t~p h<;1psinh.Vin d~ ma chung ta seo

2.5.2 TIm t~ P hQ'p sinh

Trong mt,lc nfi¥ se trinh bay cach tim mQt ~p hqp sinh kh6ng tfim thuong voi s6 phfin tU cang it cang t6t cua m~ng suy di~n. Truoc he't, ta co th6 tim mQt t~p hqp sinh b~ng phuong phap thtl' dfin duqc th6 hi~n bC1ithu~t toan sail day:

Thudt tmin 2.6: TIm mQt t~p hqp sinh Strong m?ng suy di~n (A, D).

Buoc 1: S +- {} II B~t cho S ban d~u la r6ng

Bu'oc 2: Tinh baa dong Closure(S) cua ~p h<;1pS. Bu'oc 3: Ki6m ITa so sanh Closure(S) va A.

If Closure(S)

=

Else Begin

ChQn ffiQtphffn tiYx E A-S; S +- S u {x}; Quay I?i Bu'ac 2;

End

Thu?t tmin nffy se cho ta mQt t?P hejp sinh vOi dQ phuc t?P

O(1A12.IDl.min(lAI,IDI)),do dQ phuc t?P cua phep loan t?P hejp lIen cac t?P hejp

thuQctinh cua A la O(IAI)va dQ phuc t?P eua thu?t loan tim bao dong eua mQt t~phejptren m?ng suy di€n (A, D) la O(lAI.IDl.min(lAI,IDI)).

Ta co th€ xay d1;1'ngmQt thu?t loan t6t hon thu?t loan lIen b~ng each thie't I?p ffiQt "bi€u d6 (hay d6 thi) phan ea'p" eua mQt m?ng suy di~n. Kh6ng lam ma't tinh t6ng quat ta co th€ gia sll' cae lu?t suy di~n co phffn ke't lu?n g6m I phffn tit

- Dinh nghla 2.8: Cho mQtm~lllgsuy di€n (A, D) ma m6i lu?t suy di~n co phffn

ke't lu?n g6m I phffn tll'. Ta xay d1;1'ngmQt d6 thi dinh huang Graph(A, D) nhu'

sail:

(1) T?p hejp dlnh g6m ta't ea cae thuQe tinh va ta't ea cae lu?t suy di~n, tue la

AuD.

(2) Ung vai m6i lu?t r : hypothesis(r) -+ goal(r) ta thie't I?p mQt t?P hejp

~ '

edges(r) g6m ta't eel cae cling dinh huang (x, r) va (r, y) thoa x E

hypothesis(r) va y E goal(r) mQt each tudng ling. T?p hejp cae e?nh eua d6 thi Graph(A, D) la hejp ta't eel cae t?P hejp edges(r) vai r eh?y trong t?P D.

Trang tru'ong hejp lIen d6 thi Graph(A, D) ta co degin(x) :::;1 vai mQi x E A, thl ta co th€ hi€u ngffm cae dlnh thuQc D va xet mQt d6 thi thu gQn GraphD(A)

g6m:

(1) T?p hejp dlnh la t?P hejp cae thuQe tinh A.

(2) T~p hQp c~nh g6m ta"tca cac cling (x,y) thoa man di~u ki~n: Co (duy

nha"t) mQt lu~t r saG cho goal(r)

=

Vi du 2.14: M~ng suy di~n (A, D) vai A

=

rl: A, a=> R; r2: A, B => C; r3: R, C => c; r4: R, B => b; r5: a, b, c => p; r6: a, b, c, p ~ S

se eo d6 thi Graph(A, D) co t~p hQp dlnh 13

Au D

=

va t?P hQpcac cling la

{(A,rl), (a,rl), (rl,R), (A,r2), (B,r2), (r2,C), (R,r3), (C,r3), (r3,c), (R,r4), (B,r4), (r4,b),

(a,r5), (b,r5), (c,r5), (r5,p), (a,r6), (b,r6), (c,r6), (p,r6), (r6,S) }

Tren d6 thi Graph(A, D) m6i x E A co dung mOt cling huang tai, va d6 thi thu gQn GraphD(A)co t~p dlnh la

A

=

va t~ P hQp c~nh 13

{(A,R), (a,R), (A,C), (B,C), (R,e), (C,c), (R,b), (B,b), (a,p), (b,p), (c,p), (a,S), (b,S), (c,S), (p,S)}

~ .