1 LING 6932 Spring 2007 LING 6932 Topics in Computational Linguistics Hana Filip Lecture 2: Regular Expressions, Finite State Automata

2 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 k - Cached - Similar pages Slide from Dorr/Monz

4 LING 6932 Spring 2007 Regular Expressions Regular expressions are CASE SENSITIVE The pattern /woodchuck/ will not match the string Woodchuck Disjunction /[wW]oodchuck/ Slide from Dorr/Monz

5 LING 6932 Spring 2007 Regular Expressions Ranges [A-Z] Slide from Dorr/Monz

6 LING 6932 Spring 2007 Regular Expressions  Negation / [^a]/ ^: caret ‘match any single character except a’ Slide from Dorr/Monz

7 LING 6932 Spring 2007 Regular Expressions Operators ?, * and + ? (0 or 1) /woodchucks?/  woodchuck or woodchucks /colou?r/  color or colour * (0 or more) /oo*h!/  oh! or ooh! or ooooh! + (1 or more) /o+h!/  oh! or ooh! or ooooh!  related to the immediately preceding character or regular expression *+*+ Stephen Cole Kleene  Wild card. /beg. n/  begin or began or begun any character between beg and n (except a carriage return) Slide from Dorr/Monz

8 LING 6932 Spring 2007 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/  “on my way” “Monday” (boundary) /\Bon\b/  “automaton” (non-boundary) Slide from Dorr/Monz

9 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 Advanced operators Regular expression operators for counting REMatch {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 LING 6932 Spring 2007 Advanced operators To refer to characters that are special themselves precede them with a backslash RE MatchExample 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 LING 6932 Spring 2007 Advanced operators Slide from Dorr/Monz

18 LING 6932 Spring 2007 Substitutions and Memory Substitution operator s/regexp1/regexp2/ (UNIX, Perl) s/colour/color/ s/colour/color/g Substitute as many times as possible! Case insensitive matching s/colour/color/i Slide from Dorr/Monz

19 LING 6932 Spring 2007 Substitutions and Memory Substitutions “the Xer they were, the Xer they will be” constrain the two X’s to be the same string /the (.*)er they were, the $1er they will be/ /the (.*)er they (.*), the $1er they $2/ Using numbered memories or registers: $1, $2, etc. used to refer back to matches An extended feature of regular expressions Slide from Dorr/Monz

20 LING 6932 Spring 2007 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 LING 6932 Spring 2007 Eliza-style regular expressions 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/ Step 1: replace first person with second person references 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 Three Views Three equivalent formal ways to look at what we’re up to (thanks to Martin Kay) Regular Expressions Regular Languages Finite State Automata

24 LING 6932 Spring 2007 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 LING 6932 Spring 2007 Finite-state Automata (Machines) /^baa+!$/ q0q0 q1q1 q2q2 q3q3 q4q4 baa! a state transition final state baa! baaa! baaaa! baaaaa!... Slide from Dorr/Monz

26 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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: q 0 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 LING 6932 Spring 2007 Yet Another View State-transition table

29 LING 6932 Spring 2007 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 LING 6932 Spring 2007 Recognition Traditionally, (Turing’s idea, 1936) this process is depicted with a tape.

31 LING 6932 Spring 2007 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 LING 6932 Spring 2007 Input Tape baaa q0q0 q1q1 q2q2 q3q3 q3q3 q4q4 ! baa ! a ACCEPT Slide from Dorr/Monz

33 LING 6932 Spring 2007 Input Tape aba!b q0q baa ! a REJECT Slide from Dorr/Monz

34 LING 6932 Spring 2007 Adding a failing state q0q0 q1q1 q2q2 q3q3 q4q4 baa! a qFqF a ! b ! b! b b a ! Slide from Dorr/Monz

35 LING 6932 Spring 2007 Tracing D-Recognize

36 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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 LING 6932 Spring 2007 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.