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version 5
04.11.06
DFA
KMP
DFA∑ },,,,{ 0 FqQ δ
Q
∑
δ
∑→× QQ:δ
0q
F
Q={“on”,”off”}
∑= }"_{" pressedkey
"")"_","("
"")"_","("
onpressedkeyoff
offpressedkeyon
=
=
δ
δ
""0 offq =
""offF =
DFA
2
∈∈=
∈=
=
∑∑∑
+awawqwaq
aaqaq
,)),,(~
(),(~
),(),(~
),(~
δδδ
δδ
εδ
LDFA
}),(~
|{ 0 FwqwL ∈= δ
"
},01|{ *∑∈== yxyxwwL
•
3
00
321
}1,0{
},,{
qF
qqqQ
=
=
=
=
∑
),( aqδ
0q2q0q
3q2q2q
3q3q3q
)(3 nSn3q
3
)(2 nSn2q
n-1
)(0 nSn0q
n-1
n
n=0
•
nkkS ,,2,1,0)(3 =∀)(2 kS)(0 kS
)1(3 +nS)1(2 +nS)1(0 +nS
• 3qn+1
3q
3q
)(3 nS3q
),( aqδn2q)(2 nS
nn+12q3qn+1
),( aqδ
• 2qn+1
n
• 0qn+1
nn=0
L
∑=
=
}1,0{
}3|{ bydividablenumberbinaryiswwL
4
5
LDFA
LW
}|{
}\|{
}|{
}|{
*
LwWandworWwandLwwWL
LwwL
WwandLwwWL
WworLwwWL
∉∈∉∈=⊕
∈=
∈∈=∩
∈∈=∪
∑
LWWL∪∩�WLו
� תשג ו י ר א ל ו ג ר ת ו .פ
LLת י ר א ל ו ג ר � .ג
LW WL⊕ת י ר א ל ו ג ר ה פ .ש
KMP
LALA
L
A
A
6
)(4 nSn4q
)(3 nSn3q
)(2 nSn2q
)(1 nSn1q
w
w|w|+1
KMP
wy
wywy
w
ywy
O((|y|-|w|)|w|)
KMP
• :preprocessing
w
O(|w|)
7
• y
O(|y|)
• O(|w|+|y|)
•
� KMP
� CLRS
� KMP
NFA NFADFA
DFANFA
NFA
- NFA
DFA
NFA
NFANFA ∑ },,,,{ 0 FqQ δ
Q
∑
0q
F
δ
∑ →× )(: QPQ εδ U
.
8
∑ →× )(: QPQ εδ U
0q1q,0q0q
2qΘ1q
ΘΘ2q
NFA
NFA
NFA
),,,...,,,( 12110 +kkk qrqrqrqi
iq1+iqir
wkrrw ...1=
LNFA }|{ FinendwhichwforpathlegalexistwL =
DFA-NFA
NFA }'1'0|{ stwoexactlyorsofnumberevenancontainswwL =
9
NFA
}110|{ substringthecontainnotdoeswwL =
NFA
}010000|{ substringasoreithercontainswwL =
DFANFADFA
NFA"" DFANFA⊆
DFANFA
DFANFA
DFANFA
10
LNFA
NFADFADFA
DFANFA
L
DFADFA
LWWL∪ת י ר א ל ו ג ר ה פ .ש
NFA
L Lת י ר א ל ו ג ר � .ג
LW WL⊕ת י ר א ל ו ג ר ה פ .ש
}|{
......if 121121
LwwL
aaaawthenaaaaw
RR
kk
R
kk
∈=
== −−
L RLת י ר א ל ו ג ר � .ג
}|{* WlandLwlwWL ∈∈=
LWWL *ת י ר א ל ו ג ר ה פ .ש
NFA
NFA
