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Finite-State Methods in Natural Language Processing

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Finite-State Methods in Natural Language Processing

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Finite-State Methods in Natural Language Processing

Lauri Karttunen

LSA 2005 Summer Institute

July 18, 2005

- July 18:
- Intro to computational morphology
- XFST

- Readings
- Lauri Karttunen, “Finite-State Constraints”, The Last Phonological Rule. J. Goldsmith (ed.), pages 173-194, University of Chicago Press, 1993.
- Karttunen and Beesley, “25 Years of Finite-State Morphology”
- Chapter 1: “Gentle Introduction” (B&K)

- Regular expressions
- More on XFST

- Chapter 2: “Systematic Introduction”
- Chapter 3: “The XFST interface”

- July 25
- Concatenative morphotactics
- Constraining non-local dependencies

- Readings
- Chapter 4. “The LEXC Language”
- Chapter 5. “Flag Diacritics”

- Non-concatenative morphotactics
- Reduplication, interdigitation

- Chapter 8. “Non-Concatenative Morphotactics”

- August 1
- Realizational morphology

- Readings
- Gregory T. Stump. Inflectional Morphology. A Theory of Paradigm Structure. Cambridge U. Press. 2001. (An excerpt)
- Lauri Karttunen, “Computing with Realizational Morphology”, Lecture Notes in Computer Science, Volume 2588, Alexander Gelbukh (ed.), 205-216, Springer Verlag. 2003.

- Optimality theory

- Paul Kiparsky “Finnish Noun Inflection” Generative Approaches to Finnic and Saami Linguistics, Diane Nelson and Satu Manninen (eds.), pp.109-161, CSLI Publications, 2003.
- Nine Elenbaas and René Kager. "Ternary rhythm and the lapse constraint". Phonology 16. 273-329.

- There will be three assignments, given on each Wednesday. The first two are to be turned in by the following Monday, the last one by the following Friday.
- You will get credit for the course if you solve at least two of the three assignments. The solutions will involve programming in the xfst scripting language. The problems will be easy to solve if you have attended the class.
- If you have any problems in doing the assignments, Michael Wagner and I will be happy to help you.

Copies will arrive in the

Linguistics Department

tomorrow afternoon.

You can purchase a copy there

tomorrow as soon as the books

have arrived.

Starting Wednesday, books can

Be purchased from our TA,

Michael Wagner.

The price is $35.

With the book comes a

software CD for Solaris,

Linux, MacOSX and Windows

operating systems.

- http://lsa.dlp.mit.edu/Class/207
- You can use this username and password to access materials:
- Username: LSA207
- Password: seunsehi207
- Your are free to copy, modify and use the slides for whatever purpose provided that you give appropriate credit to the original source.
- The readings for Wednesday’s class (“Finite-State Constraints”, “25 Years of Finite-State Morphology” and “Gentle Introduction” (Chapter 1 of B&K book) are posted on the web site).

- The software on the Book CD dates back to the Spring of 2003. For an update, point your browser to
- http://www.stanford.edu/~laurik/.lsa207/

- Please read the README file and the License Agreement before downloading the software.
- The updated software supports UTF-8 encoded Unicode input/output. The Book version supports only Latin-1 (ISO-8859-1).
- The XFST application will be available locally on some computers (ask Michael).
- Check out the web site for the Book:
- http://www.fsmbook.com/

- Domains of Application
- Tokenization
- Sentence breaking
- Spelling correction
- Morphology (analysis/generation)
- Phonological disambiguation (Speech Recognition)
- Morphological disambiguation (“Tagging”)
- Pattern matching (“Named Entity Recognition”)
- Shallow Parsing

- Types of Finite-State Systems
- Classical (non-weighted) automata
- Weighted (associated with weights in a semi-ring)
- Binary relations (simple transducers)
- N-ary relations (multi-tape transducers)

Analysis

Generation

hang V Past

leaf N Pl

leave N Pl

leave V Sg3

leaves

hanged

hung

- Morphotactics
- Words are composed of smaller elements that must be combined in a certain order:
- piti-less-ness is English
- piti-ness-less is not English

- Words are composed of smaller elements that must be combined in a certain order:
- Phonological alternations
- The shape of an element may vary depending on the context
- pity is realized as pitiin pitilessness
- die becomes dy in dying

- The shape of an element may vary depending on the context

- The relation between the surface forms of a language and the corresponding lexical forms can be described as a regular relation.
- A regular relation consists of ordered pairs of strings.
- leaf+N+Pl : leaveshang+V+Past : hung

- Complex regular relations can be derived from simple relations.

- A regular relation can be defined using the metalanguage of regular expressions.
- [{talk} | {walk} | {work}]
- [%+Base:0 | %+SgGen3:s | %+Progr:{ing} | %+Past:{ed}];
- A regular expression can be compiled into a finite-state transducer that implements the relation computationally.

Finite-state transducer

+Base:

final

state

+3rdSg:s

a

t

+Progr:i

:n

:g

a

l

k

w

o

r

+Past:e

:d

initial

state

Regular expression

- [{talk} | {walk} | {work}]
- [%+Base:0 | %+SgGen3:s | %+Progr:{ing} | %+Past:{ed}];

work+3rdSg --> works

+Base:

+3rdSg:s

a:a

t:t

+Progr:i

:n

:g

a:a

l:l

k:k

w:w

o:o

r:r

+Past:e

:d

+Base:

+3rdSg:s

a:a

t:t

+Progr:i

:n

:g

a:a

l:l

k:k

w:w

o:o

r:r

+Past:e

:d

talked --> talk+Past

start xfst

- xfst[0]: regex
- [{talk} | {walk} | {work}]
- [% +Base:0 | %+SgGen3:s | %+Progr:{ing} | %+Past:{ed}];

% xfst

xfst[0]:

compile a regular expression

xfst[1]: apply up walked

walk+Past

apply the result

xfst[1]: apply down talk+SgGen3

talks

vouloir +IndP +SG + P3

Finite-state transducer

veut

citation form

inflection codes

v

o

u

l

o

i

r

+IndP

+SG

+P3

v

e

u

t

inflected form

- Bidirectional: generation or analysis
- Compact and fast
- Comprehensive systems have been built for over 40 languages:
- English, German, Dutch, French, Italian, Spanish, Portuguese, Finnish, Russian, Turkish, Japanese, Korean, Basque, Greek, Arabic, Hebrew, Bulgarian, …

Morphotactics

Lexicon

Regular Expression

Lexicon

FST

Lexical Transducer

(a single FST)

Compiler

composition

Rules

Regular Expressions

Rule

FSTs

Alternations

f

a

t

+Adj

+Comp

t

e

f

a

t

r

fst 1

fst 2

fst n

Lexical form

Ordered sequence

of rewrite rules

(Chomsky & Halle ‘68)

can be modeled

by a cascade of

finite-state transducers

Johnson ‘72

Kaplan & Kay ‘81

Intermediate form

...

Surface form

- C. Douglas Johnson (1972) showed that
- phonological rewrite rules are interpreted in a way that makes them less powerful than they appear
- rewrite rules can be modeled by finite transducers
- for any two finite transducers applied in a sequence there exists an equivalent single transducer (Schützenberger 1961).

- Johnson’s result was ignored and forgotten, rediscovered by Ronald M. Kaplan and Martin Kay at Xerox around 1980.

- Phonological rewrite rules are not as powerful as they appear because of the constraint that a rule does not apply to its own output. (Johnson 1972, Kaplan&Kay 1980).

k a N p a n

k a m p a n

k a m m a n

N -> m / _ p

p -> m / m _

N:m

2

p

m

N:m

?

m

0

?

p

1

N

N

m

p

1

?

m

0

?

p:m

k a N p a n

k a m p a n

k a m m a n

0 0 0 2 0 0 0

0 0 0 1 0 0 0

3

0

2

1

N:m

p:m

k a N p a n

k a m m a n

N:m

m

0 0 0 3 0 0 0

m

?

?

p

p:m

N:m

m

N

?

N

N

fst n

Lexical form

...

fst 2

fst 1

Surface form

Set of parallel

of two-level rules (constraints)

compiled into finite-state automata

interpreted as transducers

Koskenniemi ‘83

Koskenniemi 1983

Chomsky&Halle 1968

Lexical form

Lexical form

rule 1

rule 1

...

rule 2

rule 1

rule n

Intermediate form

Surface form

intersect

...

FST

rule n

Surface form

compose

- ? u: ty ? A s
- ? u: t I y ? A s
- ? u: t u y ? a s
- ? o:t u y ? a s

Epenthesis

Harmony

Yawelmani Vowel Harmony Kisseberth 1969

Lowering

? u:t 0 y ? A s

? o: t u y ? a s

Epenthesis: Insert u or i (underspecification)

Harmony: Rounding next to a round V of the same height.

Lowering: Long u always realized as long o.

Underlying representation controls all three alternations.

- Two different ways of decomposing the complex relation between lexical and surface forms into a set of simpler relations that can be more easily understood and manipulated.
- One approach may be more convenient than the other for particular applications.

{a}

Language

or

Relation

describes

encodes

Regular Expression

Finite-State Network

compiles into

a

a

xfst[0]: define Cat {cat} | {tiger} | {lion};

defined Cat: 640 bytes. 11 states, 12 arcs, 3 paths. ...

xfst[0]:

xfst[0]: set verbose off

xfst[0]: define Dog {dog} | {spaniel} | {poodle};

xfst[0]: regex Cat | Dog ;

xfst[1]: apply up

apply up> dog

dog

apply up> panther

apply up>

apply up> END;

xfst[1]: define Animal

xfst[0]:

xfst[0]: regex Cat & Dog;

xfst[1]: print net

Sigma: a c d e g i l n o p r s t

Size: 13, Label Map: Default

Net:

Flags: deterministic, pruned, minimized, epsilon_free, ...

s0: (no arcs)

xfst[1]:

xfst[1]: pop

xfst[0]:

xfst[0]: regex Animal - Dog;

xfst[1]: push Cat

xfst[2]: test equivalent

1, (0=NO,1=YES)

xfst[2]: clear

xfst[0]:

Network

c

l

e

a

r

e

v

e

f

a

t

h

xfst[0]: read text

clear

clever

ear

ever

fat

father

^D

432 bytes. 10 states, 12 arcs, 6 paths.

read text < file

read regex {clear}|{clever}|{ear}|{ever}|{fat}|{father} ;

- Symbols
- Simple symbols vs. symbol pairs
- Special symbols: ANY, EPSILON

- Common regular expression operators
- concatenation, union, intersection, negation, composition

- Xerox operators
- contains, restriction, replacement

a

- Single and multicharacter symbols
- a, b, c, … , +Adj, +SG, ^Fin

- Special symbols
- 0 EPSILON
- ?ANY

- Symbols vs. symbol pairs
- In general, no distinction is made between
- athe language {“a”}
- a:athe identity relation {<“a”, “a”>}

- In general, no distinction is made between

- concatenation
- * +iteration
- |union
- &intersection*
- ~ \ -complementation*, minus*
- .x. :crossproduct
- .o.composition
- * = not applicable to regular relations because the result may not be encodable by a finite-state network.

?

b:B

c:C

a:A

[a:A | b:B | c:C | d:D | … ]*

d:D

- A*zero or more contatenations of A
- A+one or more concatenations of A
- ?*the universal language/
- the universal identity relation

a

a

?

a

a

?

?

?

- \Aany single symbol that is not in A
- \? the null language
- ~Aany string that is not in A
- a
- \a
- Sigma: a, ?
- ~a

b:y

a:x

c:0

- A .x. BThe relation that maps every string in A to every string in B, and vice versa
- A:BSame as [A .x. B].

a b c .x. x y

[a b c] : [x y]

{abc}:{xy}

b

a

c

b:B

a:A

c:C

b:B

c:C

a:A

d:D

- A .o. BThe relation C such that if A maps x to y and B maps y to z, C maps x to z.

{abc} .o. [a:A | b:B | c:C | d:D]*

- $containment
- => restriction
- -> @-> replacement
- Make it easier to describe complex languages and relations without extending the formal power of finite-state systems.

a

?

?

a

$a

[?* a ?*]

b

a => b _ c

b

?

a

c

“Anyamust be preceded byb

and followed byc.”

?

c

c

~[~[?* b] a ?*] & ~[?* a ~[c ?*]]

Equivalent expression