Fst morphology
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FST Morphology. Miriam Butt October 2003. Based on Beesley and Karttunen 2003. Recap. Last Time: Finite State Automata can model most anything that involes a finite amount of states. We modeled a Coke Machine and saw that it could also be thought of as defining a language.

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FST Morphology

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Fst morphology

FST Morphology

Miriam Butt

October 2003

Based on Beesley and Karttunen 2003


Recap

Recap

Last Time: Finite State Automata can model most anything that involes a finite amount of states.

We modeled a Coke Machine and saw that it could also be thought of as defining a language.

We will now look at the extension to natural language more closely.


A one word language

A One-Word Language

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A three word language

A Three-Word Language

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Analysis a successful match

Analysis: A Successful Match

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Input:

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Rejects

Rejects

The analysis of libro, tigra, cant, mesas will fail.

Why?

Use: for example for a spell checker


Transducers beyond accept and reject

Transducers: Beyond Accept and Reject

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Transducers beyond accept and reject1

Transducers: Beyond Accept and Reject

Analysis Process:

  • Start at the Start State

  • Match the input symbols of string against the lower-side symbol on the arcs, consuming the input symbols and finding a path to a final state.

  • If successful, return the string of upper-side symbols on the path as the result.

  • If unsucessful, return nothing.


A two level transducer

A Two-Level Transducer

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Input:

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Output:

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A lexical transducer

A Lexical Transducer

+PresInd

+Sg

+Verb

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+1P

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Input:

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Output:

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+Verb

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One Possible Path through the Network


A lexical transducer1

A Lexical Transducer

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+Sg

+Noun

+Masc

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Input:

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Output:

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+Noun

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Another Possible Path through the Network

(found through backtracking)


Why transducer

Why Transducer?

General Definition: Device that converts energy from one form to another.

In this Context: Device that converts one string of symbols into another another string of symbols.


The tags

The Tags

Tags or Symbols like +Noun or +Verb are arbitrary: the naming convention is determined by the (computational) linguist and depends on the larger picture (type of theory/type of application).

One very successful tagging/naming convention is the Penn Treebank Tag Set


The tags1

The Tags

What kind of Tags might be useful?


Generation vs analysis

Generation vs. Analysis

The same finite state transducers we have been using for the analysis of a given surface string can also be used in reverse: for generation.

The XRCE people think of analysis as lookup, of generation of lookdown.


Generation lookdown

Generation --- Lookdown

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+Sg

+Verb

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+1P

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Input:

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Output:

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Generation lookdown1

Generation --- Lookdown

Analysis Process:

  • Start at the Start State and the beginning of the input string

  • Match the input symbols of string against the upper-side symbols on the arcs, consuming the input symbols and finding a path to a final state.

  • If successful, return the string of lower-side symbols on the path as the result.

  • If generation is unsuccessful, return nothing.


Tokenization

Tokenization

General String Conversion: Tokenizer

Task: Divide up running text into individual tokens

  • couldn’t -> could not

  • to and from -> to-and-fro

  • ,,, -> ,

  • The farmer walked -> The^TBfarmer^TBwalked


Sharing structure and sets

Sharing Structure and Sets

Networks can be compressed quite cleverly (p. 16-17).

Sets:

FST Networks are based on formal language theory. This includes basics of set theory:

membership, union, intersection,

subtraction, complementation


Some basic concepts representations

Some Basic Concepts/Representations

Empty Language

Empty-String Language


Some basic concepts representations1

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Some Basic Concepts/Representations

A Network for an Infinite Language

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A Network for the Universal Language


Relations

Relations

Ordered Set: members are ordered.

Ordered Pair: <A,B> vs. <B,A>

  • Relation: set whose members are ordered pairs

    • Family Trees (p. 21)

    • { <“cantar+Verb+PresInd+1P+Sg”, “canto”>,

    • <“canto+Noun+Masc+Sg”, “canto”>,

    • ... }


Relations1

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Relations

An Infinite Relation:.

Identity Relation: <“canto”, “canto”>


Basic set operations

Basic Set Operations

  • union(p. 24)

  • intersection (p. 25)

  • subtraction (p. 25)


Concatenation

Concatenation

One can also concatenate two existing languages (finite state networks with one another to build up new words productively/dynamically).

This works nicely, but one has to write extra rules to avoid things like: *trys, *tryed, though trying is okay.


Concatenation1

Concatenation

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Network for the Language {“work”}

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Network for the Language {“s”, “ed”, “ing”}


Concatenation2

Concatenation

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Concatenation of the two networks

What strings/language does this result in?


Composition

Composition

Composition is an operation on two relations.

Composition of the two relations <x,y> and <y,z> yields <x, z>

Example: <“cat”, “chat”> with <“chat”, “Katze”> gives <“cat”, “Katze”>


Composition1

Composition

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Composition2

Composition

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Merging the two networks


Composition3

Composition

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The Composition of the Networks

What is this reminiscent of?


Composition rule application

Composition + Rule Application

Composition can be used to encode phonology-style rules.

E.g., Lexical Phonology assumes several iterations/levels at which different kinds of rules apply.

This can be modeled in terms of cascades of FST transducers (p. 35).

These can then be composed together into one single transducer.


Next time

Next Time

  • Begin working with xfst

  • Now: Exercises 1.10.1, 1.10.2, 1.10.4

  • Optional: 1.10.3


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