1. March 1, 2009 Dr. Muhammed Al-mulhem 1 ICS 482 Natural Language Processing Regular Expression and Finite Automata Muhammed Al-Mulhem March 1, 2009

2. Dr. Muhammed Al-mulhem 2 Regular Expressions Regular expression (RE): A formula for specifying a set of strings. String: A sequence of alphanumeric characters (letters, numbers, spaces, tabs, and punctuation).

3. March 1, 2009 Dr. Muhammed Al-mulhem 3 Regular Expression Patterns RE String matched woodchucks “interesting links to woodchucks and lemurs” a “Sarah Ali stopped by Mona’s” Ali says, “My gift please,” Ali says,” book “all our pretty books” ! “Leave him behind!” said Sami

4. March 1, 2009 Dr. Muhammed Al-mulhem 4 Specify Options and Range using [ ] and - REMatch [wW]ood Wood or wood [abc] “a”, “b”, or “c” [A-Z]an uppercase letter [a-z]a lowercase letter [0-9]a single digit

5. March 1, 2009 Dr. Muhammed Al-mulhem 5 RE Operators REDescription a* Zero or more a’s a+ One or more a’s a? Zero or one a’s [ab]* Zero or more a’s or b’s. Matches aaa.., ababab.., bbbb.. [0-9]+ Sequence of one or more digits.. Wildcard expression-matches any single character. \b Matches a word boundary. Matches the but not other

6. March 1, 2009 Dr. Muhammed Al-mulhem 6 Sidebar: Errors Find all instances of the word “the” in a text. –/the/ What About ‘The’ –/[tT]he/ What about ‘Theater”, ‘Another’

7. March 1, 2009 Dr. Muhammed Al-mulhem 7 Sidebar: Errors The process we just went through was based on: –Matching strings that we should not have matched (there, then, other) False positives –Not matching things that we should have matched (The) False negatives

8. March 1, 2009 Dr. Muhammed Al-mulhem 8 Sidebar: Errors Reducing the error rate for an application often involves two efforts –Increasing accuracy (minimizing false positives) –Increasing coverage (minimizing false negatives)

9. March 1, 2009 Dr. Muhammed Al-mulhem 9 Regular expressions Basic regular expression patterns Perl-based syntax (slightly different from other notations for regular expressions) Disjunctions [abc] Ranges [A-Z] Negations [^Ss] Optional characters ?, + and * Wild cards. Anchors \b and \B Disjunction, grouping, and precedence |

10. March 1, 2009 Dr. Muhammed Al-mulhem 10 Preceding character or nothing using ?

11. March 1, 2009 Dr. Muhammed Al-mulhem 11 10/10/201511 Wildcard

12. March 1, 2009 Dr. Muhammed Al-mulhem 12 10/10/201512 Negation using ^

13. March 1, 2009 Dr. Muhammed Al-mulhem 13 Writing correct expressions Exercise: write a regular expression to match the English article “the”: /the/ missed ‘The’ included ‘the’ in ‘others’ /[tT]he/ /\b[tT]he\b/ Missed ‘the25’ ‘the_’ /[^a-zA-Z][tT]he[^a-zA-Z]/ Missed ‘The’ at the beginning of a line

14. March 1, 2009 Dr. Muhammed Al-mulhem 14 A more complex example Exercise: Write a Perl regular expression that will match “any PC with more than 500MHz and 32 Gb of disk space for less than $1000”:

15. March 1, 2009 Dr. Muhammed Al-mulhem 15 Example Price –/$[0-9]+/ # whole dollars –/$[0-9]+\.[0-9][0-9]/ # dollars and cents –/$[0-9]+(\.[0-9][0-9])?/ #cents optional –/\b$[0-9]+(\.[0-9][0-9])?\b/ #word boundaries Specifications for processor speed –/\b[0-9]+ *(MHz|[Mm]egahertz|Ghz|[Gg]igahertz)\b/ Memory size –/\b[0-9]+ *(Mb|[Mm]egabytes?)\b/ –/\b[0-9](\.[0-9]+) *(Gb|[Gg]igabytes?)\b/ Vendors –/\b(Win95|WIN98|WINNT|WINXP *(NT|95|98|2000|XP)?)\b/ –/\b(Mac|Macintosh|Apple)\b/

16. March 1, 2009 Dr. Muhammed Al-mulhem 16 Advanced Operators – Aliases for common ranges Underscore: Correct figure 2.6

17. March 1, 2009 Dr. Muhammed Al-mulhem 17 \ to Reference special characters

18. March 1, 2009 Dr. Muhammed Al-mulhem 18 Operators for counting

19. March 1, 2009 Dr. Muhammed Al-mulhem 19 Finite State Automata FSA recognizes the regular languages represented by regular expressions –SheepTalk: /baa+!/ Directed graph with labeled nodes and arc transitions Five states: q0 the start state, q4 the final state, 5 transitions q0 q4 q1q2q3 ba a a!

20. March 1, 2009 Dr. Muhammed Al-mulhem 20 Formally FSA is a 5-tuple consisting of –Q : set of states {q0,q1,q2,q3,q4} –  : an alphabet of symbols {a,b,!} –q0 : A start state –F : a set of final states in Q {q4} –  (q,i) : a transition function mapping Q x  to Q q0 q4 q1q2q3 ba a a!

21. March 1, 2009 Dr. Muhammed Al-mulhem 21 FSA recognizes (accepts) strings of a regular language –baa! –baaa! –baaaa! –… A rejected input aba!b q0 q4 q1q2q3 ba a a!

22. March 1, 2009 Dr. Muhammed Al-mulhem 22 State Transition Table State Input ba! 01ØØ 1Ø2Ø 2Ø3Ø 3Ø34 4ØØØ q0 q4 q1q2q3 ba a a! FSA can be represented with State Transition Table

23. March 1, 2009 Dr. Muhammed Al-mulhem 23 Non-Deterministic FSAs for SheepTalk q0 q4 q1q2q3 ba a a! q0 q4 q1q2q3 baa! 

24. March 1, 2009 Dr. Muhammed Al-mulhem 24 A language is a set of strings String: A sequence of letters Languages

25. March 1, 2009 Dr. Muhammed Al-mulhem 25 Tracing FSA - Initial Configuration Input String

26. March 1, 2009 Dr. Muhammed Al-mulhem 26 Reading the Input

27. March 1, 2009 Dr. Muhammed Al-mulhem 27

28. March 1, 2009 Dr. Muhammed Al-mulhem 28

29. March 1, 2009 Dr. Muhammed Al-mulhem 29

30. March 1, 2009 Dr. Muhammed Al-mulhem 30 Output: “accept”

31. March 1, 2009 Dr. Muhammed Al-mulhem 31 Rejection

32. March 1, 2009 Dr. Muhammed Al-mulhem 32

33. March 1, 2009 Dr. Muhammed Al-mulhem 33

34. March 1, 2009 Dr. Muhammed Al-mulhem 34

35. March 1, 2009 Dr. Muhammed Al-mulhem 35 Output: “reject”

36. March 1, 2009 Dr. Muhammed Al-mulhem 36 Another Example

37. March 1, 2009 Dr. Muhammed Al-mulhem 37

38. March 1, 2009 Dr. Muhammed Al-mulhem 38

39. March 1, 2009 Dr. Muhammed Al-mulhem 39

40. March 1, 2009 Dr. Muhammed Al-mulhem 40 Output: “accept”

41. March 1, 2009 Dr. Muhammed Al-mulhem 41 Rejection

42. March 1, 2009 Dr. Muhammed Al-mulhem 42

43. March 1, 2009 Dr. Muhammed Al-mulhem 43

44. March 1, 2009 Dr. Muhammed Al-mulhem 44

45. March 1, 2009 Dr. Muhammed Al-mulhem 45 Output: “reject”

46. March 1, 2009 Dr. Muhammed Al-mulhem 46 Formalities Deterministic Finite Accepter (DFA) : set of states : input alphabet : transition function : initial state : set of final states

47. March 1, 2009 Dr. Muhammed Al-mulhem 47 About Alphabets Alphabets means we need a finite set of symbols in the input. These symbols can and will stand for bigger objects that can have internal structure.

48. March 1, 2009 Dr. Muhammed Al-mulhem 48 Input Aplhabet

49. March 1, 2009 Dr. Muhammed Al-mulhem 49 Set of States

50. March 1, 2009 Dr. Muhammed Al-mulhem 50 Initial State

51. March 1, 2009 Dr. Muhammed Al-mulhem 51 Set of Final States

52. March 1, 2009 Dr. Muhammed Al-mulhem 52 Transition Function

53. March 1, 2009 Dr. Muhammed Al-mulhem 53

54. March 1, 2009 Dr. Muhammed Al-mulhem 54

55. March 1, 2009 Dr. Muhammed Al-mulhem 55

56. March 1, 2009 Dr. Muhammed Al-mulhem 56 Transition Function

57. March 1, 2009 Dr. Muhammed Al-mulhem 57 Extended Transition Function (Reads the entire string)

58. March 1, 2009 Dr. Muhammed Al-mulhem 58

59. March 1, 2009 Dr. Muhammed Al-mulhem 59

60. March 1, 2009 Dr. Muhammed Al-mulhem 60

61. March 1, 2009 Dr. Muhammed Al-mulhem 61 Observation: There is a walk from to with label

62. March 1, 2009 Dr. Muhammed Al-mulhem 62 Example accept

63. March 1, 2009 Dr. Muhammed Al-mulhem 63 Another Example accept

64. March 1, 2009 Dr. Muhammed Al-mulhem 64 More Examples accept trap state

65. March 1, 2009 Dr. Muhammed Al-mulhem 65 = { all substrings with prefix } accept

66. March 1, 2009 Dr. Muhammed Al-mulhem 66 = { all strings without substring }

67. March 1, 2009 Dr. Muhammed Al-mulhem 67 Regular Languages A language is regular if there is a DFA such that All regular languages form a language family

68. March 1, 2009 Dr. Muhammed Al-mulhem 68 Example The language is regular:

69. March 1, 2009 Dr. Muhammed Al-mulhem 69 Finite State Automata Regular expressions can be viewed as a textual way of specifying the structure of finite-state automata.

70. March 1, 2009 Dr. Muhammed Al-mulhem 70 More Formally You can specify an FSA by enumerating the following things. –The set of states: Q –A finite alphabet: Σ –A start state –A set of accept/final states –A transition function that maps QxΣ to Q