1. Thopson NFA Presenter: Yuen-Shuo Li Date: 2014/5/7 Department of Computer Science and Information Engineering National Cheng Kung University, Taiwan R.O.C.

2. Introduction A regular expression (regex or regexp for short) is a special text string for describing a search pattern. National Cheng Kung University CSIE Computer & Internet Architecture Lab 2

3. Introduction Regular expression grammar National Cheng Kung University CSIE Computer & Internet Architecture Lab 3 SyntaxExample Any character except[\^$.|?*+()a matches a.. matches x or (almost) any other character | (abc|def|xyz) matches abc, defor xyz * “ab*c" matches “ac“, “abc“, “abbc”, “abbbc”,... + “a+" matches “a“, “aa“, “aaa”, “aaa”,... ?abc? matches abc or ab [][abc] matches a, b or c {n} a{3} matches aaa {n,m}{n,m} where n >= 0 and m >= n

4. Introduction In automata theory, a nondeterministic finite automaton (NFA), or nondeterministic finite state machine, is a finite state machine that does not require input symbols for state transitions is capable of transitioning to zero or two or more states for a given start state and input symbol. National Cheng Kung University CSIE Computer & Internet Architecture Lab 4 ε a a ε

5. Introduction Thompson's Construction Algorithm (TCA) derives a nondeterministic finite automaton (NFA) from any regular expression by splitting it into its constituent subexpressions, from which the NFA will be constructed using a set of rules. National Cheng Kung University CSIE Computer & Internet Architecture Lab 5

6. The expression ε is converted to National Cheng Kung University CSIE Computer & Internet Architecture Lab 6 ε e.g. A? => (A|ε)

7. A symbol a of the input alphabet is converted to National Cheng Kung University CSIE Computer & Internet Architecture Lab 7 a

8. The union expression RE1|RE2 is converted to National Cheng Kung University CSIE Computer & Internet Architecture Lab 8 a ε RE1 ε ε RE2 ε

9. The concatenation expression RE1 ． RE2 is converted to National Cheng Kung University CSIE Computer & Internet Architecture Lab 9 a RE1 RE2

10. The concatenation expression RE1 ． RE2 is converted to National Cheng Kung University CSIE Computer & Internet Architecture Lab 10 a RE1 RE2 or

11. The Kleene star expression RE* is converted to National Cheng Kung University CSIE Computer & Internet Architecture Lab 11 ε RE ε ε ε

12. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 12 A

13. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 13 A B

14. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 14 A B AB

15. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 15 AB

16. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 16 AB CD

17. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 17 AB CD ε ε ε ε

18. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 18 A B C D ε ε ε ε

19. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 19 A B C D ε ε ε ε ε ε ε ε E

20. (AB|CD)E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 20 A B C D ε ε ε ε ε ε ε ε E

21. National Cheng Kung University CSIE Computer & Internet Architecture Lab 21 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ (AB|CD) E* RegexParse TreeNFA

22. National Cheng Kung University CSIE Computer & Internet Architecture Lab 22 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ http://matt.might.net/articles/parsing-regex-with-recursive-descent/

23. National Cheng Kung University CSIE Computer & Internet Architecture Lab 23 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ

24. A National Cheng Kung University CSIE Computer & Internet Architecture Lab 24 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ

25. AB National Cheng Kung University CSIE Computer & Internet Architecture Lab 25 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ

26. AB ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 26 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ

27. AB ． C National Cheng Kung University CSIE Computer & Internet Architecture Lab 27 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ

28. AB ． CD National Cheng Kung University CSIE Computer & Internet Architecture Lab 28 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ

29. AB ． CD ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 29 ． ｜ * ． Ａ Ｂ Ｃ Ｄ Ｅ

30. AB ． CD ． | National Cheng Kung University CSIE Computer & Internet Architecture Lab 30 ． ｜ * ． Ａ Ｂ Ｃ Ｄ Ｅ

31. AB ． CD ． |E National Cheng Kung University CSIE Computer & Internet Architecture Lab 31 ． ｜ * ． Ａ Ｂ Ｃ Ｄ Ｅ

32. AB ． CD ． |E* National Cheng Kung University CSIE Computer & Internet Architecture Lab 32 ． ｜ * ． Ａ Ｂ Ｃ Ｄ Ｅ

33. AB ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 33 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ

34. AB ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 34 ． ｜ * ． ． Ａ Ｂ Ｃ Ｄ Ｅ postfix notation

35. AB ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 35

36. AB ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 36 stack

37. B ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 37 stack A

38. B ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 38 stack A A

39. B ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 39 stack A

40. ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 40 stack A B

41. ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 41 stack A B B

42. ． CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 42 stack A B

43. CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 43 stack A B ．

44. CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 44 stack A ． B

45. CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 45 stack ． B A

46. CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 46 stack BA

47. CD ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 47 stack B A

48. D ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 48 stack B A C

49. D ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 49 stack B A C C

50. D ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 50 stack B A C

51. ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 51 stack B A C D D

52. ． |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 52 stack B A C D

53. |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 53 stack B A C D ．

54. |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 54 stack B A C ． D

55. |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 55 stack B A ． D C

56. |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 56 stack B A DC

57. |E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 57 stack B A D C

58. E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 58 stack B A D C |

59. E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 59 stack B A | DC

60. E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 60 stack | DC BA

61. E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 61 stack A B C D ε ε ε ε

62. E* ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 62 stack A B C D ε ε ε ε

63. * ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 63 stack A B C D ε ε ε ε E

64. * ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 64 stack A B C D ε ε ε ε E E

65. * ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 65 stack A B C D ε ε ε ε E

66. ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 66 stack A B C D ε ε ε ε E *

67. ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 67 stack A B C D ε ε ε ε * E

68. ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 68 stack A B C D ε ε ε ε * ε ε ε ε E

69. ． National Cheng Kung University CSIE Computer & Internet Architecture Lab 69 stack A B C D ε ε ε ε * ε ε ε ε E

70. National Cheng Kung University CSIE Computer & Internet Architecture Lab 70 A B C D ε ε ε ε ε ε ε ε E

71. Regular Expression to NFA DFA http://hackingoff.com/compilers/regular-expression-to- nfa-dfa http://hackingoff.com/compilers/regular-expression-to- nfa-dfa National Cheng Kung University CSIE Computer & Internet Architecture Lab 71