LING 6932 Topics in Computational Linguistics

1. LING 6932 Topics in Computational Linguistics Hana Filip Lecture 2: Regular Expressions, Finite State Automata

2. Regular expressions • formulas for specifying text strings • How can we search for any of these strings? • woodchuck • woodchucks • Woodchuck • Woodchucks Figure from Dorr/Monz slides

3. Regular Expressions • Basic patterns of regular expressions • Perl-based syntax (slightly different from other notations for regular expressions as used in UNIX, for example) • /Woodchuck/ matches any string containing the substring Woodchuck, if your search application returns entire lines, for example ‘/’ notation used by Perl, NOT part of the RE Google: Woodchuck Draft Cider Producers of Woodchuck Draft Cider in Spingfield, VT. www.woodchuck.com/ - 17k - Cached - Similar pages Slide from Dorr/Monz

4. Regular Expressions • Regular expressions are CASE SENSITIVE • The pattern /woodchuck/will not match the string Woodchuck • Disjunction /[wW]oodchuck/ Slide from Dorr/Monz

5. Regular Expressions • Ranges[A-Z] Slide from Dorr/Monz

6. Regular Expressions • Negation/[^a]/ ^: caret ‘match any single character except a’ Slide from Dorr/Monz

7. *+ Stephen Cole Kleene Regular Expressions • Operators ? , * and + • ?(0 or 1) /woodchucks?/  woodchuckorwoodchucks /colou?r/  colororcolour • *(0 or more) /oo*h!/ oh!orooh!orooooh! • + (1 or more) • /o+h!/ oh!orooh!orooooh! • related to the immediately preceding character or regular expression • Wild card ./beg.n/  begin or began or begun any character between beg and n (except a carriage return) Slide from Dorr/Monz

8. Regular Expressions • Anchors ^ and $ start of line • /^[A-Z]/  “Ramallah, Palestine” • /^[^A-Z]/  “¿verdad?” “really?” end of line • /\.$/  “It is over.” • /.$/  ? • Boundaries \b and \B • /\bon\b/  “onmy way” “Monday” (boundary) • /\Bon\b/  “automaton” (non-boundary) Slide from Dorr/Monz

9. Disjunction, Grouping, Precedence • Disjunction | • /yours|mine/  “it is either yours or mine” • /gupp(y|ies)/  “guppy” or “guppies” • Column 1 Column 2 Column 3 …How do we express this? /Column[0-9]*/  ‘space’ /(Column[0-9]*)*/ NOT a RE character matches the word Column, followed by one number, followed by zero or more spaces, the whole pattern repeated any number of times (zero or more times) Slide from Dorr/Monz

10. Disjunction, Grouping, Precedence • Operator Precedence Hierarchy • Parenthesis () • Counters * + ? • Sequences and anchors the ^my end$ • Disjunction | • REs are greedy! They always match the largest string they can Slide from Dorr/Monz

11. Example • Find me all instances of the word “the” in a text. • /the/ Misses capitalized examples • /[tT]he/ Returns “other” or “theology” • /\b[tT]he\b/ matches “the” or “The” • /[^a-zA-Z][tT]he[^a-zA-Z]/ • /(^|[^a-zA-Z])[tT]he[^a-zA-Z]/ Matches “the_” or “the25”

12. Errors • The process we just went through was based on two fixing kinds of errors • Not matching things that we should have matched (The) • False negatives • Matching strings that we should not have matched (there, then, other) • False positives

13. Errors cont. • We’ll be telling the same story for many tasks • Reducing the error rate for an application often involves two antagonistic efforts: • Increasing accuracy (minimizing false positives) • Increasing coverage (minimizing false negatives).

14. More complex RE example • Regular expressions for prices • /$[0-9]+/ • Doesn’t deal with fractions of dollars • /$[0-9]+\.[0-9][0-9]/ • Doesn’t allow $199, not at a word boundary • /\b$[0-9]+(\.[0-9]0-9])?\b)/

15. Advanced operators Regular expression operators for counting RE Match {n} exactly n occurrences of the previous character or expression {n,m} from n to m occurrences of the previous character or expression {n, } at least n occurrences of the previous character or expression /a\.{24}z/ a followed by 24 dots followed by z

16. Advanced operators To refer to characters that are special themselves precede them with a backslash RE Match Example Strings Matched \* an asterisk “*” “K*A*P*L*A*N” \. a period “.” “Dr.Livingston, I presume.” \? A question mark “?” “Would you light my candle?” \n a newline \t tab

17. Advanced operators Slide from Dorr/Monz

18. Substitutions and Memory • Substitution operator s/regexp1/regexp2/ (UNIX, Perl) Substitute as many times as possible! s/colour/color/ s/colour/color/g s/colour/color/i Case insensitive matching Slide from Dorr/Monz

19. Substitutions and Memory • Substitutions “the Xer they were, the Xer they will be” constrain the two X’s to be the same string Using numbered memories or registers: $1,$2, etc. used to refer back to matches An extended feature of regular expressions /the (.*)er they were, the $1er they will be/ /the (.*)er they (.*), the $1er they $2/ Slide from Dorr/Monz

20. Eliza [Weizenbaum, 1966] User: Men are all alike ELIZA: IN WHAT WAY User: They’re always bugging us about something or other ELIZA: CAN YOU THINK OF A SPECIFIC EXAMPLE? User: Well, my boyfriend made me come here ELIZA: YOUR BOYFRIEND MADE YOU COME HERE User: He says I’m depressed much of the time ELIZA: I AM SORRY TO HEAR THAT YOU ARE DEPRESSED

21. Eliza-style regular expressions Step 1: replace first person with second person references s/.* YOU ARE (depressed|sad) .*/I AM SORRY TO HEAR YOU ARE \1/ s/.* YOU ARE (depressed|sad) .*/WHY DO YOU THINK YOU ARE \1/ s/.* all .*/IN WHAT WAY/ s/.* always .*/CAN YOU THINK OF A SPECIFIC EXAMPLE/ s/\bI(’m | am)\b/YOU ARE/g s/\bmy\b/YOUR/g S/\bmine\b/YOURS/g Step 2: use substitutions that look for relevant patterns in the input and create an appropriate output (reply) Step 3: use scores to rank possible transformations Slide from Dorr/Monz

22. Summary on REs so far • Regular expressions are perhaps the single most useful tool for text manipulation • Dumb but ubiquitous • Eliza: you can do a lot with simple regular-expression substitutions

23. Three Views • Three equivalent formal ways to look at what we’re up to (thanks to Martin Kay) Regular Expressions Finite State Automata Regular Languages

24. Finite State Automata • Terminology: Finite State Automata, Finite State Machines, FSA, Finite Automata • Regular expressions are one way of specifying the structure of finite-state automata. • FSAs and their close relatives are at the core of most algorithms for speech and language processing.

25. baa! baaa! baaaa! baaaaa! ... /^baa+!$/ a b a a ! q0 q1 q2 q3 q4 finalstate state transition Finite-state Automata (Machines) Slide from Dorr/Monz

26. Sheep FSA • We can say the following things about this machine • It has 5 states • At least b, a, and ! are in its alphabet • q0 is the start state • q4 is the final (= accept) state • It has 5 transitions

27. More Formally: Defining an FSA • You can specify an FSA by enumerating the following things. • a finite set of states: Q • a finite alphabet of symbols:  • the start state: q0 • The set of accepting/final states: F such that FQ • A transition function (q,i) that maps Qx to Q Given a state qQ and an input symbol i, (q,i) returns a new state q’Q.

28. Yet Another View • State-transition table

29. Recognition • Recognition is the process of determining if a string should be accepted by a machine • Or… it’s the process of determining if a string is in the language we’re defining with the machine • Or… it’s the process of determining if a regular expression matches a string

30. Recognition • Traditionally, (Turing’s idea, 1936) this process is depicted with a tape. http://www.cs.princeton.edu/introcs/75turing/

31. Recognition - Execution • Start in the start state • Examine the current input in the active cell • Consult the table: a finite table of instructions (a state transition diagram) that specifies exactly what action the machine takes at each step • Go to a new state and update the tape pointer. • Until you run out of tape.

32. q4 q0 q1 q2 q3 q3 a b a a a b a a ! ! 0 1 2 3 4 Input Tape ACCEPT Slide from Dorr/Monz

33. q0 a b a ! b a b a a ! 0 1 2 3 4 Input Tape REJECT Slide from Dorr/Monz

34. ! ! b ! b ! b b a a qF Adding a failing state a b a a ! q0 q1 q2 q3 q4 Slide from Dorr/Monz

35. Tracing D-Recognize

36. Key Points • Deterministic means that at each point in processing there is always one unique thing to do (no choices). D-recognize is a simple table-driven interpreter • The algorithm is universal for all unambiguous languages. • To change the machine, you change the table.

37. Key Points • Deterministic Pattern Example: Consider a set of traffic lights; the sequence of lights is red - red/amber - green - amber - red. The sequence can be pictured as a state machine, where the different states of the traffic lights follow each other. Each state is dependent solely on the previous state, so if the lights are green, an amber light will always follow - that is, the system is deterministic. Deterministic systems are relatively easy to understand and analyse, once the transitions are fully known.

38. Key Points • Crudely therefore… matching strings with regular expressions (a la Perl) is a matter of • translating the expression into a machine (table) and • passing the table to an interpreter

39. Recognition as Search • You can view this algorithm as state-space search. • States are pairings of tape positions and state numbers. • Operators are compiled into the table • Goal state is a pairing with the end of tape position and a final accept state

40. Generative Formalisms • A formal Language is a model m which can both generate and recognize all and only the strings of a formal language; each string is composed of symbols from a finite set of symbols (alphabet) L(m) ‘a formal language L characterized by the model m’ • Finite-state automata define formal languages (without having to enumerate all the strings in the language) • The term Generative is based on the view that you can run the machine as a generator to get strings from the language.

41. Generative Formalisms • FSAs can be viewed from two perspectives: • Acceptors that can tell you if a string is in the language (recognition) • Generators to produce all and only the strings in the language (production)

42. Summary • Regular expressions are just a compact textual representation of FSAs • Recognition is the process of determining if a string/input is in the language defined by some machine. • Recognition is straightforward with deterministic machines.