Title: Introduction to the xfst Interface
1Introduction to the xfst Interface
- Review
- Introduction to Morphology
- Relations and Transducers
- Introduction to xfst
2Basic Formal-Language Review
- What is a Symbol?
- What is an Alphabet?
- What is a string (word)?
- What is a Language?
- What basic operations can be performed on Sets?
- What basic operations can be performed on
Languages?
3Formal Languages and Natural Languages
- Any set of strings is a formal language
- L1 a, aa, aaa, aaaa, aaaaa,
- L2 zzmy, niwhiuhew, sjehuiwheu
- L3 dog, cat, elephant
- The systems that we write will accept or map
words in a formal language. - In practical natural-language processing, we try
to make these formal languages as close as
possible to a natural language, e.g. Swahili.
I.e. we try to model a natural language, as
perfectly as possible, in our grammars. - We write our grammars using xfst and lexc.
4Concatenation can form Real Words
work talk walk
ing ed s
Root Language
Suffix Language
The concatenation of the Suffix language after
the Root language.
working worked works talking talked talks walking
walked walks
5Concatenation can also form Bad Words
ing ed s
try plot wiggle
Suffix Language
Root Language
Raw Concatenation Result/Level/Language
trys tryed trying plots ploted ploting
wiggles wiggleed wiggleing tries
tried trying plots plotted plotting
wiggles wiggled wiggling Desired Final
Result/Level/Language
6Inuktitut
- Parismutnngaujumaniraqlauqsimanngitjunga
- Pari mu nngau juma nira lauq si ma nngit tunga
- Paris Paris
- mut terminalis-case
- nngau direction-to
- juma want
- niraq declare that
- lauq past
- si perfective
- ma resulting state
- nngit negative
- junga 1P pres. indic
I never said that I wanted to go to Paris
7Concatenative-Agglutinative (Aymara)
- Lexical utamana-kapxaraki-iwa
- Surface uta ma n ka p xa rak i wa
- uta house (noun stem)
- ma 2nd person possessive (your)
- na in (case suffix)
- -ka locative (also verbalizes)
- p plural
- xa perfect aspect
- raki also
- -i 3rd person present tense
- wa topic (primary emphasis)
- also they are in your house
8Morphology
- In most languages, morphemes are just
concatenations of symbols from the alphabet of
the language. - In most languages, words are just concatenations
of morphemes. - But raw concatenation often gives us abstract,
morphophonemic, not-yet-correct words. - There are alternations between the raw
concatenations and the desired final words. - There are two challenges in natural-language
Morphology - Morphotactics describe word-formation
- Alternation describe mappings between raw
concatenations and final forms - Both can be modeled and computed using
finite-state methods
9Transducers
- Recall that finite-state transducers can map
from one string of symbols to a different string
of symbols.
c a n t a r
Verb PInd 1P Sg
c a n t ? ?
? o ? ?
We can also use transducers to map between
abstract, not-yet-correct forms (usually built by
simple concatenation) and correct forms.
w i g g l e
i n g
w i g g l ?
i n g
10Regular Relations
- A Regular Language is a set of strings, e.g.
cat, fly, big . - An ordered pair of strings, notated ltupper,
lowergt, relates two strings, e.g. ltwiggleing,
wigglinggt. - A Regular Relation is a set of ordered pairs of
strings, e.g. - ltcatN, catgt , ltflyN, flygt , ltflyV,
flygt, ltbigA, biggt - Or
- ltcat, catsgt , ltzebra, zebrasgt ,
ltdeer, deergt, ltox, oxengt, ltchild,
childrengt - The set of upper-side strings in a relation is a
Regular Language. - The set of lower-side strings in a relation is a
Regular Language. - A Regular Relation is a mapping between two
Regular Languages. Each string in one of the
languages is related to one or more strings of
the other language. - A Regular Relation can be encoded in a
Finite-State Transducer (FST).
11Relations, Analysis and Generation
- Given a transducer (relation), and a string, we
can see the mappings of the relation via Analysis
and Generation
Apply the transducer in a downward direction to
the upper-side string to perform Generation.
Upper-side string c a n t a r Verb PInd 1P
Sg
c a n t a r
Verb PInd 1P Sg
c a n t
o
Apply the transducer in an upward direction to
the lower-side string to perform Analysis.
Lower-side string c a n t o
12Transducers encode Finite-State Relations
- Let a Relation X include the ordered string pairs
- ltcantarVerbPInd1PSg, cantogt,
- ltcantoNounMascSg, cantogt
- What is the upper-side Language of this Relation?
- What is the lower-side Language of this Relation?
- How can such a relation be encoded?
- What do you get when you analyze the string
canto? - What do you get when you generate from the string
cantarVerbPInd1PSg?
13Rules and Infinite Relations
- One or both of the Languages related by a
Relation can be infinite, e.g. the relation that
relates lower-case words to their upper-case
versions - lta, Agt, ltaa, AAgt, ltdog, DOGgt,
bB
cC
Apply this network in a downward direction to the
input string cad. What is the output?
aA
Etc, (assume arcs for all other symbols in the
alphabet)
dD
14Alternation Rules
- We will write finite-state rules to describe
alternations between abstract morphophonemic
words and well-formed surface words. - These rules compile into finite-state transducers
(relations) that can be used to compute these
mappings. - Typically the upper language of a rule FST is the
Universal Language, the set of all possible
strings. - Typically the lower language is like the upper
language, except for the alternations controlled
by the rule. - Strings that dont match the rule are mapped
unchanged.
15Rule Application Composition
- Composition is an operation that merges two
transducers vertically. Let X be a transducer
that contains the single ordered pair lt dog,
chiengt. Let Y be a transducer that contains
the single ordered pair ltchien, Hundgt. The
composition of X over Y, notated X .o. Y, is the
relation that contains the ordered pair ltdog,
Hundgt . - Composition merges any two transducers. If the
shared middle level has a non-empty intersection,
then the result will be a non-empty relation. - Rule application is done via composition.
- Composition is a difficult topic that we will
return to many times. Read pp 28-34 and do
exercise 1.10.3 on page 37.
16Review Basic Concepts
- Language a set of strings/words
- Regular Language a set of string/words that can
be generated using concatenation, union,
iteration and similar operations - Simple Finite-State Automaton (Acceptor) a
finite-state machine that accepts/recognizes a
regular language - Regular Relation a mapping between two regular
languages - Finite-State Transducer (FST) a two-level
finite-state automaton that maps between two
regular languages (performs look-up and
generation)
17Regular Expressions
- A compact formula for describing a regular
language or regular relation. - The regular-expression language is a
metalanguage. - Think of regular expressions as the programming
language of xfst - Each implementation of regular expressions is
slightly different (Python, Perl, emacs, ) - We will have to learn the Xerox flavor of regular
expressions as used in xfst.
18Regular Expressions Denoting a Language
Regular Expression
describes
compiles into
Regular Language
Finite-State Automaton (acceptor)
accepts/recognizes
19Regular Expression Denoting a Relation
Regular Expression
describes
compiles into
Regular Relation
Finite-State Transducer
maps
20Introduction to xfst
- xfst is an interface giving access to the
finite-state operations (algorithms such as
union, concatenation, iteration, intersection). - xfst includes a powerful and efficient
regular-expression compiler. - xfst includes the lookup operation (apply up)
and the generation operation (apply down) so
that we can test our networks. For small
examples, we can also print out all the words in
the language using the command print words. - We have to learn the Xerox regular-expression
metalanguage.
21Xerox Regular-Expression Operators I
- a a simple symbol
- c a t a CONCATENATION of three symbols
- c a t grouping
brackets - ? denotes any single symbol
- Noun or Noun
- Verb or Verb
- Adj or Adj
- single
symbols with multicharacter print names - (aka multicharacter symbols)
- cat Beware this will be compiled by xfst as a
single multicharacter symbol - cat explosion brackets equivalent to c a t
22Xerox Regular Expression Operators II
-
- 0 two ways to denote the empty (zero-length)
string - Now, where A and B are arbitrarily complex
regular expressions - A bracketing equivalent to A
- A B union
- (A) optional equivalent to A 0
- A B intersection
- A B concatenation (N.B. the space between A and
B) - A - B subtraction
23Xerox Regular-Expression Operators III
- A Kleene star zero or more iterations
- A Kleene plus one or more iterations
- ? The Universal Language
- A The complement of language A equivalent to
? - A - ? The empty language (i.e. it contains no
strings at all, not even the zero-length
string) - the literal plus-sign symbol
- the literal asterisk symbol
- and similarly for ?, (, ), , etc.
24Denoting Relations
- A .x. B the cross-product relates every
string in A to every string in B, and vice
versa e.g. - g o .x. w e n t relates go and went
- ab shorthand for a .x. b
- Pls shorthand for Pl .x. s
- Pasted shorthand for Past .x. e d
- Proging shorthand for Prog .x. i n g
25Useful Abbreviations
- A denotes the language of all strings that
contain A equivalent to ? A ? , e.g. - b denotes the language of all strings that
contain a b anywhere - A/B denotes the language of all strings in A,
ignoring any strings from B, e.g. - a/b contains a, aa, aaa, ba, ab,
aba, ... - \A any single symbol, minus strings in A i.e.
? - A , e.g. - \b denotes any single symbol, except a b
- Beware NOT to be confused with
- A the complement of A i.e. ? - A
26Basic xfst interface commands
- UnixPrompt xfst
- xfstgt help
- xfstgt help union net
- xfstgt exit
- xfstgt read regex d o g c a t
- xfstgt read regex lt myfile.regex
- xfstgt apply up dog
- xfstgt apply down dog
- xfstgt pop stack
- xfstgt clear stack
- xfstgt save stack myfile.fsm
27xfst saves networks in a LIFO stack
- xfstgt read regex d o g c a t
- or
- xfstgt read regex lt myfile.regex
- causes the compiled network to be pushed onto
the stack. When you type - xfstgt pop stack
- the top network is popped off the stack and
discarded. When you type - xfstgt apply up dog
- the top network on the stack is applied in an
upward direction (lookup) on the string dog,
and the related string or strings are printed.
When you type - xfstgt clear stack
- the entire stack is popped and left empty. When
you type - xfstgt save stack myfile.fsm
- the contents of the stack are written in binary
(compiled) form to the indicated file.
28Setting Variables
- xfstgt define Myvar
- pops the top network off of the stack and saves
it as the value of Myvar, which can be used in
subsequent regular expressions - xfstgt define Myvar2 d o g c a t
- assigns a value to Myvar2 without modifying the
stack. It is equivalent to the two commands - xfstgt read regex d o g c a t
- xfstgt define Myvar2
- xfstgt undefine Myvar
- undefines Myvar and recycles the memory
29 Using Variables in Regular Expressions
- xfstgt define var1 b i r d f r o g d o g
- xfstgt define var2 d o g c a t
- You can now use var1 and var2 in subsequent
regular expressions - xfstgt define var3 var1 var2
- xfstgt define var4 var1 var2
- xfstgt define var5 var1 var2
- xfstgt define var6 var1 - var2
30Performing network operations on the stack
- xfstgt read regex d o g c a t
- xfstgt read regex m o u s e r a t
- xfstgt read regex d e e r s q u i r r e l
- xfstgt union net
- union net will pop its arguments off of the
stack one at a time, perform the union operation,
and push the result back onto the stack, leaving
just one network on the stack. Enter the command
words to see the resulting language.
31The xfst Stack
- Assume that two networks have already been pushed
onto the stack. - If we then invoke a stack-based operation like
union net, the xfst algorithm pops its first
argument from the top of the stack, then the
second argument - NetA NetB
NetA
NetB
32Remember that the stack is last-in, first-out
(LIFO)
- Ordered operations like minus net and compose
net are often difficult to get right. E.g.
Assume that we want to compute A - B on the
stack. Try this - xfstgt define A d o g c a t m o u s e r
a t - xfstgt define B d o g m o u s e e l e p h
a n t - Now push the arguments onto the LIFO stack in the
right order and invoke minus net. If you have
a defined variable X, you can push its value onto
the stack using - xfstgt push X
- or
- xfstgt read regex X
- What is your answer? Type words to see the
language of the resulting network.
33The xfst Stack and Ordered Operations
- To perform NetA NetB, the B net must be pushed
onto the stack first, then the A net, so that
they can be popped off in the reverse order. - When performing operations on the stack, try to
visualize the stack itself. - NetA - NetB
NetA
NetB
34A little concatenation example
- xfstgt define Root w a l k t a l k w
o r k - xfstgt define Prefix 0 r e
- xfstgt define Suffix 0 s e d i n g
- xfstgt read regex Prefix Root Suffix
- xfstgt words
- xfstgt apply up walking
- Try to get the same result by starting with the
same three definitions and then pushing them on
the stack, invoking concatenate net to perform
the concatenation. Remember that concatenation
is an ordered operation.
35xfst file types
- Regex files contain only a regular expression,
terminated with a semicolon and newline. - xfstgt read regex d o g c a t
- xfstgt read regex lt myfile.regex
- Binary files contain an already compiled network
or networks, e.g. - xfstgt save stack myfile.fsm
- xfstgt load stack myfile.fsm
- Script files contain a list of xfst commands
run them with source - xfstgt source myfile.script
36The Simplest Replace Rules
- Replace rules are a very powerful extension to
the regular-expression metalanguage. Here is the
simplest kind needed for the kaNpat and
Portuguese-pronunciation exercises. The arrow -gt
is typed as a hyphen followed by a right
angle-bracket. The operator consists of two
vertical bars typed together. The _ is the
underscore. - Rule Schema upper -gt lower
- upper -gt lower leftcontext _ rightcontext
- E.g.
- xfstgt read regex s -gt z a e i o
u _ a e i o u - xfstgt apply down casa
- What is this rule intended to do? What comes out?
37kaNpat example
- Assume a language that joins morpheme kaN (with
an underspecified nasal N) and morpheme pat into
the underlying or morphophonemic form kaNpat.
This language then has alternation rules that
dictate that N, when followed by p, gets realized
as m. And p, when preceded by m, gets realized
as m. The derivation looks like - Underlying input kaNpat
- Rule1 N -gt m _ p
- Output of Rule1 kampat
- Rule2 p -gt m m _
- Output of Rule2 kammat
- The composition operation (.o.) reduces the
derivational cascade of transducer networks into
a single transducer network.
38Your first cascade of rules
- xfstgt define Rule1 N -gt m _ p
- xfstgt define Rule2 p -gt m m _
- xfstgt read regex Rule1 .o. Rule2
- xfstgt apply down kaNpat
- What is the output?
- Now restart (with clear stack), define the two
Rules as shown above, push them on the stack in
the right order, and perform the composition on
the stack using compose net. What is your
result? (Remember that the networks must be
pushed in the right order.)
39Rule Abbreviations
- Multiple left-hand sides, separated by commas
- b -gt p, d -gt t, g -gt k _ ..
- Multiple right-hand sides, separated by commas
- e -gt i _ (s) .. , .. p _ r
- Use .. to refer to either the very beginning or
the very end of a word.
40Typing Accented Letters in xemacs
- The COMPOSE key is to the right of the space bar.
- COMPOSE a yields ä
- COMPOSE a á
- COMPOSE a à
- COMPOSE a â
- COMPOSE a ã
- COMPOSE c , ç
41A Trick for Testing Multiple Words
- The exercise will ask you to write a cascade of
rules that map orthographical strings to
something more like a phonemic notation. - Type the test words into a file, e.g. wordlist
- Compile your rules, compose them, and put the
result on The Stack - Test all the words using the following syntax
- xfst1 apply down lt wordlist
42Assignment
- Read Chapter 2 (The Systematic Introduction) when
you can. - For hands-on practice right now start reading
Chapter 3, doing the examples as you go along. - Do the kaNpat exercise in section 3.5.3 and the
Southern Brazilian Portuguese exercise in 3.5.4
(p. 134). - Progress to Bambona (p. 140) and Monish (p. 146)
if you can.