Knuth-Morris-Pratt

1
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
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accept state
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2
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
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a
b
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3
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0
1
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accept state
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b
b
3
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
b
a
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a
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a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
4
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
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a
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a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
5
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
a
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b
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a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
6
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
a
a
a
b
a
a
a
a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
7
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
a
a
a
b
a
a
a
a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
8
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
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a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
9
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
a
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a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
10
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
a
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b
a
a
a
a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
11
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
a
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a
a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b
12
Knuth-Morris-Pratt

• KMP algorithm. over binary alphabet
• Build DFA from pattern.
• Run DFA on text.

Search Text
a
a
a
b
a
a
b
a
a
a
b
a
a
b
a
a
a
a
a
b
a
a
a
a
a
b
a
a
a
b
a
a
a
a
a
a
b
b
3
4
5
6
0
1
2
accept state
b
b
b