Applications in finite state automata Organisation and Introduction - - PowerPoint PPT Presentation

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Applications in finite state automata Organisation and Introduction - - PowerPoint PPT Presentation

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Organisational matters Introduction Plan of the Course Literature Applications in finite state automata Organisation and Introduction Kurt Eberle kurt.eberle@uni-tuebingen.de (includes material from Karttunen, Beesley, Butt and others)

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Organisational matters Introduction Plan of the Course Literature

Applications in finite state automata

Organisation and Introduction Kurt Eberle

kurt.eberle@uni-tuebingen.de

(includes material from Karttunen, Beesley, Butt and others)

October 25, 2016

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Outline

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Goals of this session

Criteria for a certificate, times Finite State Automata? Why? Plan of the seminar

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Outline

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Hours and place of the course

◮ Tuesday, 16:15–17:45

Place: VG Wilhelmstraße / 0.01

◮ Thursday, 16:15–17:00

Place: VG Wilhelmstraße / 1.13

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Preconditions

◮ Zwischenpr¨

ufung (Courses 1st-4th semester)

◮ besides this: none

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Criteria of a successful participation I

Formal Criteria

◮ Presentation of an application ◮ (written exam) ◮ (term paper)

Informal Criteria

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Criteria of a successful participation II

◮ Class Participation!

Examination regulations of the Neuphilologische Fakult¨ at require that students attend courses regularly. If students do not attend a course meeting on more than two

  • ccasions in one semester without proper excuse (e.g. doctor’s

note), the course instructor has to give them a failing grade. Please do not put me in a position to have to fail you for this reason. If you cannot come to class, please email me ahead of time, if at all possible. You are expected to come on time. Being late without good reasons will count as not having attended a course meeting. If you own a mobile phone and carry it with you, please turn it off before class

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Criteria of a successful participation III

Helpful

◮ Please take part actively! ◮ Ask questions, tell me when you do not understand such and

such topic!

◮ If there are problems: Give feedback, email, Sprechstunde ◮ When you try out things and work on the material:

Take into account: Hofstadter’s Law:

◮ It always takes longer than you expect, even when you take

into account Hofstadter’s Law.

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Platform: Homepage of the course

Homepage

◮ URL: www.sfs.uni-tuebingen.de/˜keberle/ ◮ Key: ....

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Main Objectives

◮ Get acquainted with using FSAs for representation of

languages and mapping between languages

◮ Study of Karttunen/Beesley’s Finite State Morphology ◮ Xerox’ FSA programming machinery ◮ Focus: implementation of morphological problems/tasks ◮ Others: tokenization, shallow syntax, . . .

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Outline

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Motivation

Finite State Automata

◮ What is a finite state automaton (FSA)? ◮ example . . .

→ Karttunen/Beesley’s Cola Machine

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Cola-FSA represents . . .

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FSA formally . . .

A deterministic finite automaton M is a 5-tuple, (Q, S, d, q0, F), consisting of

◮ a finite set of states (Q) ◮ a transition function (d : QxS→Q) ◮ an initial or start state (q0 ∈ Q) ◮ a set of accept states (F ⊆ Q)

Let w = a1a2 . . . an be a string over the alphabet S. The automaton M accepts the string w if a sequence of states, r0, r1, . . . , rn, exists in Q with the following conditions:

◮ r0 = q0 ◮ ri+1 = d(ri, ai+1), for i = 0, . . . , n − 1 ◮ rn ∈ F.

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Language of a FSA

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Formally . . . Language and Grammar

◮ Formal language L ⊆ Σ∗ ◮ Word: w ∈ L ◮ Grammar: G = (V , Σ, P, S)

V : finite set of non-terminal symbols Σ : finite set of terminal symbols (V ∩ Σ = ∅) P : finite set of productions (grammar rules) S : start symbol of the grammar (S ∈ V )

◮ Productions p ∈ P have the form α → β, where

α ∈ (V ∪ Σ)∗V (V ∪ Σ)∗ and β ∈ (V ∪ Σ)∗

◮ Notational convention:

a, ai ∈ Σ; A, B, C ∈ V ; w, r ∈ Σ∗; α, β ∈ (V ∪ Σ)∗

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Formally . . .

the cola language (CL)

Grammar of the language CL: G = (V , Σ, P, S) with P: S ← Q Q ← q Q ← D D N Q ← D N D Q ← N D D D d D N N N n G generates CL: . . . {q, ddn, dnd, ndd, nndn, . . . nnnnn } Question: dd ∈ G(CL) ?

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The word problem

Task

◮ decide whether a string is a sentence/word of a language or

not!

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Motivation

Finite State Automata

◮ Finite state automata correspond to regular expressions ◮ can recognize regular languages! ◮ There are other languages ˙

.

◮ → the Chomsky hierarchy of languages

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Formal languages

Chomsky Hierarchy

◮ Type-0 grammars:

α → β (unrestricted)

◮ Type-1 grammars (context sensitive):

α → β with |α| ≤ |β| (exception: S → ε)

◮ Type-2 grammars (context free):

A → α

◮ Type-3 grammars (regular):

A → wB or A → w (right linear) and A → Bw or A → w (left linear) respectively where w ∈ Σ∗ ⇒ General phrase structure, Context sensitive, context free, regular languages

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Formal languages

Cola Language is regular

S ← q S ← 2D n S ← 3N d 2D ← D n n 2D ← D d D ← d D ← n n 3N ← D n 3N ← n d

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Chomsky Hierarchy - Examples

Context-free Languages

L = {anban | n ≥ 1} is not regular! G, Σ, S, R

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Chomsky Hierarchy - Examples

Context-sensitive Languages

L = {anbncn | n ≥ 1} is not context-free! G, Σ, S, R with

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Motivation

Finite State Automata

◮ What can be done with FSAs? ◮ → recognize regular languages:

Is (a+(c*d)) a correct arithemtic expression? (a+(c*d)) ∈ L(A)

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Motivation

Why Finite State Automata/Regular languages?

◮ Nice properties!

← closure ← decidability ← complexity

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Properties

Closure

If K and L are regular then also :

◮ K ∪ L ◮ K ∩ L ◮ -L ◮ K - L ◮ K L ◮ L*

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Properties

Decidability

If K and L are regular then decidable :

◮ w ∈ L ? ◮ L ⊆ K ? ◮ L ∩ K = {} ? ◮ L = {} ? ◮ L = Σ*

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Properties

Complexity

If L regular:

◮ space(L) = O(1)

constant space - independent of the input size

◮ linear time = O(n)

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Applications

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Another nice FSA property

Bidirectional use

◮ fsa

→ transducer: edges are labeled by ≤ symbol,symbol ≥ -relations Example: houses ↔ house+Noun+Pl

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Morphology

Two levels

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Morphology

Two levels: transducer

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Xerox and FS Morpholgy

Two levels: transducer

◮ Lauri Karttunen ◮ Kimmo Koskenniemi ◮ Martin Kay ◮ Ron Kaplan

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Xerox and FS Morpholgy

Xerox System

◮ Xerox finite state software ◮ Karttunen/Beesley Finite State Morphology ◮ http://web.stanford.edu/˜laurik/fsmbook/home.html ◮ components

◮ xfst (compiler for regular expressions) ◮ lexc (compiler for lexicon representations) ◮ . . . 36 / 43

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Morphology

Two levels: transducer

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Outline

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Our program I

Plan

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Our program II

Plan

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Outline

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Literature I

Karttunen, L., Beesley, K. Finite State Morphology. CSLI Publications, Stanford 2003 http://web.stanford.edu/˜laurik/fsmbook/home.html van Noord, Gertjan Fsa Utilities User Manual Version 6 1998 https://www.let.rug.nl/˜vannoord/Fsa/Manual/ The FSA Utilities toolbox. https://www.let.rug.nl/˜vannoord/Fsa/ https://www.let.rug.nl/˜vannoord/papers/

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Literature II

Beesley, K. Xerox Finite State Programming Course http://web.stanford.edu/˜laurik/fsmbook/lecture-notes/ Beesley2004/index.html Butt, M., B¨

  • gel, T.

Finite State Morphology Tutorial http://ling.uni-konstanz.de/pages/home/boegel/Dateien/CLT09_ tutorial.pdf Karttunen, L. Finite-State Methods in Natural Language Processing http://web.stanford.edu/˜laurik/fsmbook/LSA-207/index.html

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