Memory-Efficient Regular Expression Search Using State Merging

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Memory-Efficient Regular Expression Search Using State Merging 2019/1/13 Memory-Efficient Regular Expression Search Using State Merging IEEE INFOCOM 2007 Author: Michela Becchi Presenter: Cheng-Feng Ke Date: 2017/09/06 Department of Computer Science and Information Engineering National Cheng Kung University, Taiwan R.O.C. CSIE CIAL Lab 1

INTRODUCTION Regex No Construct a DFA Maximum Label 2019/1/13 INTRODUCTION Regex No Construct a DFA Maximum Label Weight Graphs for DFA If there is any weight > 0 Merge States Finish Yes Output a DFA obtained after merging one or more state. National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA (a[b-e][g-i]|f[g-h]j)k+ National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 1 + 1 = 2 2 <= Maximum Label Number of Sub State = 1 Number of Sub State = 1 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 Weight = 0 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 Number of Sub State = 1 Number of Sub State = 1 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 Weight = 1 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 1 + 2 = 3 3 > Maximum Label Number of Sub State = 1 Number of Sub State = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(a) Maximum Label (b) Weight Graphs for DFA 2019/1/13 (a) Maximum Label (b) Weight Graphs for DFA Maximum Label = 2 Weight = 1 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 State 3 Bitmap (256 bits) other a b c d e f g h i 1 3 Index Transition index 1 2 3 4 Transition Table Index Next State 1 2 5 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 Symbol . Destination State / Source States National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 Label 0 = > State 3 Label 1 => State 4 Input “g” Input “b” Label = 0 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 State 3 Bitmap (256 bits) other a b c d e f g h i 1 State 4 Bitmap (256 bits) other a b c d e f i j 1 State 3 Index Transition (Label) 0 (Null) 1 1 (Null) 2 2 (Null) 3 4 State 4 Index Transition (Label) 0 (Null) 1 1 (Null) 2 2 (Null) Common Transition Table Index Next State 1 2 5 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 State 3 Bitmap (256 bits) other a b c d e f g h i 1 State 4 Bitmap (256 bits) other a b c d e f i j 1 State 3 Index Transition (Label) 0 (Null) 1 1 (Null) 2 2 (Null) 3 4 State 4 Index Transition (Label) 0 (Null) 1 1 (Null) 2 2 (Null) Common Transition Table Index Next State 1 2 5 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

(c) Merge States Maximum Label = 2 2019/1/13 (c) Merge States Maximum Label = 2 State 1 Bitmap (256 bits) other a b c d e f g h i 1 State 2 Bitmap (256 bits) other a b c d e f g h i 1 State 1 Index Transition (Label) 0 (0) 1 1 (0) 2 3 4 0 (1) State 2 Index Transition (Label) 0 (0) 1 1 (1) 2 3 Common Transition Table Index Next State 1_2 1 3_4 National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

2019/1/13 EXPERIMENTAL RESULTS National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab

2019/1/13 EXPERIMENTAL RESULTS National Cheng Kung University CSIE Computer & Internet Architecture Lab CSIE CIAL Lab