ENGLISH

Finite-State Techniques: Automata, Transducers and Bimachines

Book information

Publisher
Cambridge University Press
Year
2019
ISBN
9781108756945
Language
english
Format
PDF
Filesize
4 MB (3731809 bytes)
Series
Cambridge Tracts in Theoretical Computer Science 60
Pages
315\315
Time added
2020-01-04 07:49:12

Description

Finite-state techniques provide theoretically elegant and computationally effi- cient solutions for various (hard, non-trivial) problems in text and natural language processing. Due to its importance in many fundamental applications, the theory of finite-state automata and related finite-state machines has been extensively studied and its development still continues. Contents......Page 5 Preface......Page 9 PART I FORMAL BACKGROUND......Page 12 1.1 Sets, Functions and Relations......Page 14 1.2 Lifting Functions to Sets and Tuples......Page 19 1.3 Alphabets, Words and Languages......Page 21 1.4 Word Tuples, String Relations and String Functions......Page 24 1.5 The General Monoidal Perspective......Page 27 1.6 Summing Up......Page 31 1.7 Exercises for Chapter 1......Page 32 2.1 Basic Concept and Examples......Page 34 2.2 Closure Properties of Monoidal Finite-State Automata......Page 41 2.3 Monoidal Regular Languages and Monoidal Regular Expressions......Page 44 2.4 Equivalence Between Monoidal Regular Languages and Monoidal Automaton Languages......Page 46 2.5 Simplifying the Structure of Monoidal Finite-State Automata......Page 48 2.7 Exercises for Chapter 2......Page 52 3.1 Deterministic Finite-State Automata......Page 54 3.2 Determinization of Classical Finite-State Automata......Page 57 3.3 Additional Closure Properties for Classical Finite-State Automata......Page 59 3.4 Minimal Deterministic Finite-State Automata and the Myhill–Nerode Equivalence Relation......Page 61 3.5 Minimization of Deterministic Finite-State Automata......Page 68 3.6 Coloured Deterministic Finite-State Automata......Page 73 3.7 Pseudo-Determinization and Pseudo-Minimization of Monoidal Finite-State Automata......Page 78 3.9 Exercises for Chapter 3......Page 80 4.1 Monoidal Multi-Tape Automata......Page 83 4.2 Additional Closure Properties of Monoidal Multi-Tape Automata......Page 86 4.3 Classical Multi-Tape Automata and Letter Automata......Page 88 4.4 Monoidal Finite-State Transducers......Page 91 4.5 Classical Finite-State Transducers......Page 94 4.6 Deciding Functionality of Classical Finite-State Transducers......Page 96 4.7 Summing Up......Page 101 4.8 Exercises for Chapter 4......Page 102 5.1 Deterministic Transducers and Subsequential Transducers......Page 105 5.2 A Determinization Procedure for Functional Transducers with the Bounded Variation Property......Page 111 5.3 Deciding the Bounded Variation Property......Page 119 5.4 Minimal Subsequential Finite-State Transducers: Myhill–Nerode Relation for Subsequential Transducers......Page 126 5.5 Minimization of Subsequential Transducers......Page 134 5.6 Numerical Subsequential Transducers......Page 144 5.8 Bibliographic Notes......Page 146 5.9 Exercises for Chapter 5......Page 147 6.1 Basic Definitions......Page 149 6.2 Equivalence of Regular String Functions and Classical Bimachines......Page 156 6.3 Pseudo-Minimization of Monoidal Bimachines......Page 160 6.4 Direct Composition of Classical Bimachines......Page 162 6.6 Exercises for Chapter 6......Page 167 PART II FROM THEORY TO PRACTICE......Page 170 7 The C(M) language......Page 171 7.1 Basics and Simple Examples......Page 172 7.2 Types, Terms and Statements in C(M)......Page 179 8.1 C(M) Implementations for Automata Algorithms......Page 188 8.2 C(M) Programs for Classical Finite-State Transducers......Page 205 8.3 C(M) Programs for Deterministic Transducers......Page 222 8.4 C(M) Programs for Bimachines......Page 233 9.1 Formal Construction – First Version......Page 247 9.2 Linear Computation of the Aho–Corasick Automaton......Page 255 9.3 Space-Efficient Variant – Construction of the Aho–Corasick f-Automaton......Page 257 10.1 Formal Construction......Page 264 10.2 C(M) Implementation of the Construction – First Version......Page 269 10.3 Efficient Construction of the Minimal Dictionary Automaton......Page 273 10.4 Adapting the Language of Minimal Dictionary Automata......Page 276 10.5 The Minimal Subsequential Transducer for a Finite Two-Sided Dictionary......Page 281 11 Constructing Finite-State Devices for Text Rewriting......Page 290 11.1 Simple Text Rewriting Based on Regular Relations......Page 291 11.2 Using Deterministic Machines for Simple Text Rewriting......Page 293 11.3 Leftmost-Longest Match Text Rewriting......Page 299 11.4 Regular Relations for Leftmost-Longest Match Rewriting......Page 301 References......Page 309 Index......Page 313

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