1 Introduction and preliminaries |
|
1 |
|
|
|
|
|
|
2 Many-sorted variety theorem |
|
9 |
|
|
|
2.1 Many-sorted algebras |
|
10 |
2.2 Syntactic congruences and algebras |
|
16 |
2.3 The variety theorem |
|
21 |
|
|
|
3 Positive varieties of tree languages |
|
29 |
|
|
|
3.1 Ordered algebras |
|
30 |
3.2 Positive variety theorem |
|
35 |
3.3 Generalized positive variety theorem |
|
40 |
|
|
|
4 Definability by monoids |
|
47 |
|
|
|
4.1 Algebras definable by translation monoids |
|
49 |
4.2 Tree languages definable by monoids |
|
52 |
4.3 Definability by semigroups |
|
59 |
|
|
|
5 Definability by ordered monoids |
|
65 |
|
|
|
5.1 Ordered algebras vs. ordered monoids |
|
65 |
5.2 Tree languages definable by ordered monoids |
|
69 |
5.3 Examples of varieties |
|
76 |
|
|
|
6 Tree algebras |
|
87 |
|
|
|
6.1 Binary trees and tree algebras |
|
88 |
6.2 Varieties of binary tree languages |
|
94 |
6.3 Some algebraic properties of tree algebras |
|
100 |
|
|
|
Epilogue |
|
107 |
|
|
|
|
|
|
Index of Notation |
|
109 |
|
|
|
|
|
|
References |
|
113 |