pda yang diterima bahasa bebas konteks
TRANSCRIPT
![Page 1: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/1.jpg)
Bahasa FormalPDA yang Diterima Bahasa Bebas Konteks
Pertemuan Ke-13
Sri Handayaningsih, S.T., M.T.
Email : [email protected]
Teknik Informatika
![Page 2: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/2.jpg)
TIU & TIK
Memahami konsep PDA yang diterima olehCFG antara lain :
1. PDA untuk CFG2. Deterministik PDA
2
![Page 3: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/3.jpg)
Bahasabebas konteks
(Gramer)
Bahasa ygditerimaOleh PDA
Teorema:
3
![Page 4: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/4.jpg)
Bahasabebas konteks
(Gramer)
Bahasa ygditerimaOleh PDA
Pembuktian - langkah 1:
4
Konversikan gramer bebas konteksPada PDA dengan
GM )()( MLGL
![Page 5: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/5.jpg)
Bahasabebas konteks
(Gramer)
Bahasa ygditerimaOleh PDA
Pembuktian - langkah 2:
5
Konversikan PDA ke grammer bebaskonteks dengan :G
M)()( MLGL
![Page 6: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/6.jpg)
Konversikan
Grammer bebas kontekske
Pembuktian - langkah 1
6
kePDA
![Page 7: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/7.jpg)
Bahasabebas konteks
(Gramer)
Bahasa ygditerimaOleh PDA
7
Konversikan grammer bebas konteksPada PDA dengan
GM )()( MLGL
![Page 8: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/8.jpg)
Ke PDA sebagai berikut :M
Konversi grammer G
8
M Simulasi menggunakan derivasi kiriPada G
![Page 9: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/9.jpg)
Produksi pada
wATerminal pada
aG G
Konversi grammer ke PDAG M
9
q0 q1 2qS, , $ $
wA, aa,
![Page 10: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/10.jpg)
S
GrammerDerivasi kiri
$),,(
,$),(
111
110
Sq
q
nkk
nkk
Komputasi PDASimulasi grammerDerivasi kiri
10
nkk
mk XX
11
11
,$),(
$),,(
2
111
q
XXq mnk
Variabel kiri
![Page 11: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/11.jpg)
Grammer
PDA
bSaSTbS
,,
TTaTbSaSTbS
Contoh
11
q0 q1 2qS, , $ $
TTaTbS
,,,T
bbaa
,,
![Page 12: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/12.jpg)
abTbaSTb
S
$),,($),,($),,(
$),,(,$),(
1
1
1
0
TbabqbTbbabqSTbbabq
Sababqababq
Derivsi Grammer Komputasi PDA
12
abababTab
,$),(,$),(
$),,(
$),,($),,(
$),,(
2
1
1
1
1
1
bbq
ababqTababqTbabq
![Page 13: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/13.jpg)
bSaSTbS
,,
Input
Stack
$
a ab
Time 0
b
Derivasi:
130q q1 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
![Page 14: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/14.jpg)
bSaSTbS
,,
Input
Stack
$
a ab bS
Time 0
Derivasi: S
14
q0 q1 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
![Page 15: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/15.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
a
b
ST
Time 1
Derivasi: aSTbS
15
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 16: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/16.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
a
b
ST
Time 2
aSTbS Derivasi:
16
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 17: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/17.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
bTb
Time 3
Derivasi : abTbaSTbS
17
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 18: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/18.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
bTb
Time 4
Derivasi: abTbaSTbS
18
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 19: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/19.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
b
Ta
Time 5
Derivasi: abTababTbaSTbS
19
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 20: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/20.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
b
Ta
Time 6
Derivasi: abababTababTbaSTbS
20
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 21: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/21.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
ba
Time 7
Derivasi: abababTababTbaSTbS
21
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 22: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/22.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
b
Time 8
Derivasi: abababTababTbaSTbS
22
q0 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
q1
![Page 23: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/23.jpg)
bSaSTbS
,,
Input
Stack
$
a ab b
Time 9
Derivasi: abababTababTbaSTbS
23
q0 q1 2qS, , $ $
TTaTbS
,,,
bbaa
,,
Stack
diterima
![Page 24: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/24.jpg)
Grammerdgnstring
GPDAmenerima
M
Secara Umum, dapat dilihat :
w wJika danHanya jika
24
wS*
,$),(,$),( 20 qwq
Hanya jika
sehingga )()( MLGL
![Page 25: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/25.jpg)
Kesimpulan :
Untuk setiap bahasa bebas konteksmaka PDA dapat menerima
LL
25
Bahasabebas konteks
(Gramer)
Bahasa ygditerimaOleh PDA
![Page 26: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/26.jpg)
Konversi
PDAke
Pembuktian - langkah 2
26
keGrammers Bebas konteks
![Page 27: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/27.jpg)
Bahasabebas konteks
(Gramer)
Bahasa ygditerimaOleh PDA
27
Konversika PDA ke grammer bebaskonteks denganG
M)()( MLGL
![Page 28: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/28.jpg)
Konversikan PDA keM
Grammer bebas konteks sbg berikut:G
Komputasikan Simulasi dari
28
MKomputasikan Simulasi dariDengan derivasi kiri
G
![Page 29: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/29.jpg)
Beberapa Modifikasi Penting
1. stack tdk pernah kosong selama komputasi
2. Jika hanya ada satu state yg diterimadan stack kosong ketika stack menerima string
29
3. Mempunyai transisi tanpa popping
![Page 30: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/30.jpg)
1. stack tdk pernah kosong selama komputasi
Stack
30
$a
OK
$
OK NOT OK
![Page 31: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/31.jpg)
$a
$
Penyelesain :Perkebalkan simbol baru utk menandaiStack paling bawah
#
31
$a
#$# #
![Page 32: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/32.jpg)
PDA asli
Menambahkan pada awal PDA#
initial statebaru
32
$#,$
asliinitial state
baru
![Page 33: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/33.jpg)
iq jqs,
Konversikan seluruh transisisetelah popping pada automata ygtdk selesai
$
}{#x
pop $
33
iq jqs,
halting state
xx ,}{#x
pop $
![Page 34: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/34.jpg)
PDA x,
Stack kosong}{#x
2. Modifikasi PDA pada akhir stack dgnstack kosong danmenerima state yg unik
34
fq
x,
menerima states lama
#,
MenerimaStatebaru
![Page 35: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/35.jpg)
3. Modifikasikan PDA yg tidak adatransisi popping :
iq jqy,
35
iq jq y,
}{#
![Page 36: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/36.jpg)
a, $ 0$ b, $1$
)}()(:},{{)( * wnwnbawML ba
Contoh :(modifikasi yg tidak perlu)
36
$,0q fq
a, 0 00a,1
b, 111b, 0
![Page 37: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/37.jpg)
Kontruksi Grammer
A
Pada grammer :G
Terminal :
simbols stack PDAVariabel :
a simbols input PDA
37
Terminal : a simbols input PDA
Variabel Awal : simbol bawah Stack#or$
![Page 38: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/38.jpg)
q 1qAa,transisi PDA
38
produksi Grammer aA
![Page 39: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/39.jpg)
transisi PDA q 1qmBBBAa 21,
39
produksi Grammer mBBaBA 21
![Page 40: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/40.jpg)
S
DerivasiGrammerkiri
,$),( 111 q nkk
Komputasi PDA
40
nkk
mk XX
11
11
),,(
),,(
2
111
q
XXq mnk
Variabel kiri
![Page 41: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/41.jpg)
Contoh PDA:
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0
41
0q fq
Grammer: $0$ a000 a
a1
$1$ b111 b
b0 $
![Page 42: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/42.jpg)
a $0$
DerivasiKiriGrammer :
KomputasiPDA:
$)0,,(,$),(
0
0
bbaqabbaq
42
abbaabbaabb
ab
$$1
$
),,(
,$),(
$)1,,(
,$),(
0
0
0
fq
q
aq
baq
![Page 43: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/43.jpg)
a, $ 0$ b, $1$
$Derivasi:
a ab b Time 0
43
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0
![Page 44: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/44.jpg)
a, $ 0$ b, $1$
$Derivasi:
a ab b Time 1
0
$0a
44
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 45: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/45.jpg)
a, $ 0$ b, $1$
$Derivasi:
a ab b Time 2
$0a $ab
45
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 46: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/46.jpg)
a, $ 0$ b, $1$
$Derivasi:
a ab b Time 3
$0a $ab
1
$1abb
46
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 47: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/47.jpg)
a, $ 0$ b, $1$
Derivasi:
a ab b Time 4
$ $0a $ab $1abb$abba
47
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 48: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/48.jpg)
a, $ 0$ b, $1$
Derivasi:
a ab b Time 5
kosong
abba
$ $0a $ab $1abb$abba
48
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
kosong
![Page 49: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/49.jpg)
Bagaimanapun juga, konversi grammerTdk dpt bekerja pada seluruh PDAs:
Ab,$$, Aa $, AAa
49
0q fqAb,1q $,
}1:{)( nbaML nn
![Page 50: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/50.jpg)
Ab,
0q fq
$$, Aa $, AAa
Ab,1q $,
50
Grammer: $$ aA $aAAbA$
![Page 51: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/51.jpg)
Derivasi yg buruk:
)($$$ MLaabaabaaAaAS
51
Grammer: $$ aA $aAAbA$
![Page 52: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/52.jpg)
Kontruksi Grammer Yg Benar
)( ji Aqq
Pada grammer :Gsimbol stack PDA
Variabel:
52
Terminals: simbol input pada PDA
PDA states
![Page 53: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/53.jpg)
q 1qAa,Transisi PDA
53
produksi Grammer aqAq )( 1
![Page 54: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/54.jpg)
Transisi PDA
q 1qmBBBAa 21,
54
Produksi Grammer
)())(()( 1322211 mmmm qBqqBqqBqaqAq
Utk seluruh state yg mungkinpada PDA
12 ,, mqq
+1
![Page 55: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/55.jpg)
Variabel awal : )( foZqq
Simbol stack bawah#or$
55
State awal State yg diterima
![Page 56: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/56.jpg)
Contoh ::
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0
56
$,0q fq
aqq )1( 00Produksi Grammar:
![Page 57: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/57.jpg)
Contoh :
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0
57
$,0q fq
)$)(1(|)$)(1()$(
)$)(1(|)$)(1()$(
00000
00000000
fffff
ff
qqqqbqqqqbqq
qqqqbqqqqbqq
Produksi Grammer :
![Page 58: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/58.jpg)
Contoh:
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0
58
$,0q fq
Produksi Grammer: )$( 0 fqq
![Page 59: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/59.jpg)
)$)(1(|)$)(1()$(
)$)(1(|)$)(1()$(
00000
00000000
fffff
ff
qqqqbqqqqbqq
qqqqbqqqqbqq
)1)(1(|)1)(1()1( 00000000 ff qqqqbqqqqbqq
Kesimpulan Grammer: ablestart vari:)$( 0 fqq
59
)1)(1(|)1)(1()1(
)1)(1(|)1)(1()1(
00000
00000000
fffff
ff
qqqqbqqqqbqq
qqqqbqqqqbqq
)$)(0(|)$)(0()$(
)$)(0(|)$)(0()$(
00000
00000000
fffff
ff
qqqqaqqqqaqq
qqqqaqqqqaqq
![Page 60: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/60.jpg)
)0)(0(|)0)(0()0(
)0)(0(|)0)(0()0(
00000
00000000
fffff
ff
qqqqaqqqqaqq
qqqqaqqqqaqq
bqq
aqq
)0(
)1(
00
00
60
bqq )0( 00
)$( 0 fqq
![Page 61: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/61.jpg)
)$( 0 fqq)$)(0( 000 fqqqqa
)$( qqab ,$),($)0,,(
,$),(
0
0
baqbbaq
abbaq
DerivasiGrammarKiri
KomputasiPDA
61
)$( 0 fqqab)$)(1( 000 fqqqqabb
)$( 0 fqqabba
abba ),,(
,$),(
$)1,,(
,$),(
0
0
0
fq
q
aq
baq
![Page 62: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/62.jpg)
a, $ 0$ b, $1$
)$( 0 fqqDerivasi:
a ab b Time 0
62
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0
![Page 63: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/63.jpg)
a, $ 0$ b, $1$
)$( 0 fqqDerivasi:
a ab b Time 1
0
)$)(0( 000 fqqqqa
63
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 64: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/64.jpg)
a, $ 0$ b, $1$
)$( 0 fqqDerivasi:
a ab b Time 2
)$)(0( 000 fqqqqa )$( 0 fqqab
64
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 65: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/65.jpg)
a, $ 0$ b, $1$
)$( 0 fqqDerivasi:
a ab b Time 3
)$)(0( 000 fqqqqa )$( 0 fqqab
1
)$)(1( 000 fqqqqabb
65
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 66: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/66.jpg)
a, $ 0$ b, $1$
)$( 0 fqqDerivasi:
a ab b Time 4
)$)(0( 000 fqqqqa )$( 0 fqqab)$)(1( 000 fqqqqabb )$( 0 fqqabba
66
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
$
![Page 67: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/67.jpg)
a, $ 0$ b, $1$
)$( 0 fqqDerivasi:
a ab b Time 5
)$)(0( 000 fqqqqa )$( 0 fqqab)$)(1( 000 fqqqqabb )$( 0 fqqabba abba
kosong
67
$,0q fq
a, $ 0$a, 0 00a,1
b, $1$b, 111b, 0 Stack
kosong
![Page 68: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/68.jpg)
Secara Umum:
wBAqq
)(
Jika danHanya
Grammer PDA
),,(),,( BqAwq
68
wBAqq ji )(Hanyajika ),,(),,( BqAwq ji
![Page 69: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/69.jpg)
Thus:
Jika danHanya
Grammer dggeneral PDA menerima
),,(,$),( qwq
w w
69
wqq f
)$( 0
Hanyajika ),,(,$),( 0 fqwq
![Page 70: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/70.jpg)
sehingga:
Untuk setiap PDAMerupakan grammer bebas kontekAkan menerima bahasa yg sama
70
BahasaBebas konteks
(Grammer)
bahasaditerimaOleh PDA
![Page 71: PDA Yang Diterima Bahasa Bebas Konteks](https://reader033.vdocuments.site/reader033/viewer/2022042507/5571fa7c49795991699251e7/html5/thumbnails/71.jpg)
Pustaka1. Tedy Setiadi, Diktat Teori Bahasa dan Otomata, Teknik
Informatika UAD, 20052. Hopcroft John E., Rajeev Motwani, Jeffrey D. Ullman,
Introduction to Automata Theory, Languages, andComputation, 2rd, Addison-Wesley,2000
3. Martin C. John, Introduction to Languages and Theoryof Computation, McGraw-Hill Internatioanal edition,1991
4. Linz Peter,Introduction to Formal Languages &4. Linz Peter,Introduction to Formal Languages &Automata, DC Heath and Company, 1990
5. Dulimarta Hans, Sudiana, Catatan Kuliah MatematikaInformatika, Magister Teknik Informatika ITB, 1998
6. Hinrich Schütze, IMS, Uni Stuttgart, WS 2006/07,Slides based on RPI CSCI 2400