Finite-state techniques: automata, transducers and bimachines

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