Finite State Machinery I

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Finite State Machinery - I

• Fundamentals
• Recognisers and Transducers

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Reference Outline

• Websites
• Xerox www.xrce.xerox.com/research/mltt/fst/
• Groningen grid.let.rug.nl/vannoord/FSA/fsa.html
• AT T www.research.att.com/sw/tools/fsm
• Books/Collections
• Karttunen Oflazer (2000)
• Jurafsky Martin (2000)
• Hopcraft and Ullman (1979)
• Roche and Schabes (1977)
• Classic Articles
• Kaplan and Kay (1994)
• Koskenniemi (1983)
• Johnson (1972)
• Tools
• Van Noord et al.
• Mohri et al.
• Daciuk.
• Karttunen Beesley

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Acknowledgements to

• Lauri Karttunen, Ken Beesley and colleagues at
  Xerox.
• Most materials in this tutorial are from their
  website.
• Forthcoming book Finite State Morphology Xerox
  Tools and Techniques.

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4
FS Motivation

• Chomsky hierarchy of language classes based on
  classes of descriptive notation, and also on
  asociated classes of machine.
• Chomsky (1957) dismissed FS grammars, and
  associated machinery, as fundamentally inadequate
  for the description of NL.

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Embedding

• Basic problem is not that sentences can grow to
  arbitrary length, it is that the description of a
  syntactic constitutent may embed any other
  constituents including the sentence itelf.
• The dog bit the cat.
• The dog that the man saw bit the cat.
• The dog that the man that the horse kicked saw
  bit the cat.
• etc

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On the other hand ...

• Plenty of language just ain't like that.
• Words
• Orthographic spelling.
• Phonological spelling.
• Morphology.
• Fixed expression types (e.g dqtes).
• Gross constitutent structures (e.g. the big, bad,
  blue wolf).

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Recent Application Areas for FS Technology Include

• POS Tagging
• Spell Checking
• Information Extraction
• Speech Recognition
• Text to Speech
• Spoken Dialogue
• Parsing

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Recognition of Italian Words

• The coke machine recognises words in the coke
  machine language.
• The following machine recognises two words in
  Italian.
• Recognition mechanism is language independent.

I
N
Q
U
E
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The Process of Analysis

• Start in the initial state and at the first
  symbol of the word.
• If there is an arc labelled with that symbol, the
  machine transitions to the next state, and the
  symbol is consumed.
• The process continues with successive symbols
  until .....

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10
The Process of Analysis

• One or more of these conditions holds
• A. A final state is reached
• B. All symbols are consumed
• C. There are no transitions out of a state for
  the current symbol.
• If both A and B, analysis succeeds and the word
  is recognised.
• Otherwise recognition fails.

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11
Success and Failure
C
A
S
A
I
N
Q
U
E
L
E
E
N
T
LE CASA CINQUANTA LENTEMENTE
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Transducers

• Recognisers either accept or reject a word.
• Although this is useful, networks can actually
  return more substantial information.
• This is achieved by providing networks with the
  ability to write as well as to read.

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Basic Transducer

• Each transition of a transducer is labelled with
  a pair of symbols rather than with a single
  symbol.
• Analysis proceeds as before, except that input
  symbols are matched against the lower-side
  symbols on transitions.
• If analysis succeeds, return the string of
  upper-side symbols on the path to the final state

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14
Confusing Terminology

• Lower side surface side.
• Upper side "deep" side.
• Analysis proceeds from lower to upper.
• Synthesis (generation) proceeds from upper to
  lower.

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Lexical Transducers

• In common parlance, a transducer is a device
  which converts one form of energy into another,
  e.g. a microphone converts from sound to
  electrical signals.
• Next we look at lexical transducers which convert
  one string of symbols into another.

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Lexical Transducer Example
lexical string
C
A
S
A
surface string
C
A
S
E

• Input CASE
• Output CASA

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Morphological Analysis
A
T
N
O
C
e
O
C
N
T
R
e

• Input CONTO
• Output CONTARE V 1P SG

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Remarks

• e stands for "epsilon". During analysis, epsilon
  transitions are taken freely without consuming
  any input.
• Note also single symbols with multi-character
  print names (e.g. SG).
• The order of these symbols, and the choice of
  infinitive as baseform, is determined by
  linguists.

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Exercise

• The word "conto" in Italian is also a masculine
  noun meaning (a) story and (b) bank account
• Draw the corresponding 2-level networks.
• How can the different meanings be incorporated
  into the same network

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Conto N SG
A
e
O
T
N
O
C
O
C
N
T
O
N
e
e
SG

• Input CONTO
• Output CONTO NSG

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Synthesis

• Transducers are reversible. This means that they
  can be used to perform the inverse transduction
  from an transducers.
• The process of synthesis is the inverse of
  analysis

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The Process of Synthesis

• Start at the start state and at the beginning of
  the input string.
• Match the input symbols against the upper-side
  symbols of the arcs, consuming symbols until a
  final state is reached.
• If successful, return the string of lower-side
  symbols (else nothing).

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Morphological Synthesis
A
T
N
O
C
e
O
C
N
T
R
e

• Input CONTARE V 1P SG
• Output CONTO
• N.B. e symbols are ignored on output

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Analysis and Synthesis

• Upper Side Language (Lexical Strings).
• Lower Side Language (Surface Strings).
• Transducer maps between the two.
• However large the lexical transducer may become,
  analysis and synthesis are performed by the same
  language-independent matching techniques.

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