Handbook of Formal Languages: Volume 3. Beyond Words

of Volume 3.- 1. Tree Languages.- 1. Introduction.- 2. Trees and terms.- 3. Algebraic preliminaries.- 4. Term rewriting systems.- 5. Finite tree recognizers.- 6. Regular tree grammars.- 7. Tree language operations and closure properties of Rec.- 8. Local tree languages.- 9. A Kleene theorem for tree languages.- 10. Regular tree systems.- 11. Algebraic characterizations of recognizability.- 12. Monadic second-order logic and regular tree languages.- 13. Families of special regular tree languages.- 14. The yield-function and context-free languages.- 15. Context-free tree grammars and pushdown tree recognizers.- 16. Tree transformations and tree transducers.- 17. Composition and decomposition of tree transformations.- 18. Tree transducers with regular look-ahead.- 19. Generalized syntax directed translations.- 20. Surface tree languages.- 21. The hierarchies of surface tree languages and transformational languages.- 22. Some further topics.- References.- 2. Tree-Adjoining Grammars.- 1. Introduction.- 2. Tree-adjoining grammars.- 2.1 Adjoining constraints.- 2.2 Derivation in TAG.- 2.3 Some properties of the string languages and tree sets.- 3. Lexicalized grammars.- 4. 'Lexicalization' of CFGs.- 4.1 Substitution and lexicalization of CFGs.- 4.2 Lexicalization of CFGs with TAGs.- 5. Closure of TAGs under lexicalization.- 6. Summary of lexicalization.- 7. Embedded push-down automaton (EPDA).- 7.1 Crossed dependencies.- 8. Linguistic relevance.- 9. Some variants of TAGs.- 9.1 Feature structure based TAGs.- 9.2 Synchronous TAGs.- 9.3 Probabilistic LTAGs.- 9.4 Using description trees in TAG.- 9.5 Muti-component TAGs (MCTAG).- 10. Parsing lexicalized tree-adjoining grammars (LTAG).- 10.1 Left to right parsing of TAGs.- 10.2 The algorithm.- 10.3 An example.- 10.4 Implementation.- 10.5 Complexity.- 10.6 The parser.- 10.7 Parsing substitution.- 10.8 The valid prefix property and parsing of tree-adjoining grammar.- 11 Summary.- References.- 3. Context-Free Graph Grammars.- 1. Introduction.- 2. Node and edge replacement.- 3. Hyperedge replacement grammars.- 3.1 Definitions and examples.- 3.2 Normal forms.- 3.3 Subclasses.- 4. Node replacement grammars.- 4.1 Definitions and examples.- 4.2 Subclasses and normal forms.- 4.3 Comparison of HR and NR.- 5. Monadic second order logic.- 6. Graph grammars generating strings and trees.- 7. Tree grammars generating graphs.- References.- 4. Two-Dimensional Languages.- 1. Introduction.- 2. Preliminaries.- 3. Regular expressions.- 4. Automata.- 4.1 Four-way automata.- 4.2 On-line tesselation automata.- 5. Grammars.- 6. Logic formulas.- 7. Tiling systems.- 7.1 Local two-dimensional languages.- 7.2 Tiling recognizable languages.- 7.3 Closure properties.- 7.4 Domino systems.- 7.5 Generalizations of local languages.- 8. Equivalence theorems.- 8.1 Tiling systems and automata.- 8.2 Tiling systems and logic formulas.- 8.3 Tiling systems and regular expressions.- 8.4 Comparing all families.- 9. Properties of recognizable languages.- 9.1 Necessary conditions for recognizability.- 9.2 Undecidability results.- 10. Recognizable functions.- 11. Beyond finite state recognizability.- References.- 5. Basics of Term Rewriting.- 1. Introduction.- 2. Terms.- 3. Church-Rosser properties.- 4. Orderings.- 5. Completion.- 6. Rewriting modulo a relation.- 7. Sundries.- References and further reading.- 6. ?-Languages.- 1. Introduction.- 2. Topology for languages and ?-languages.- 2.1 Cantor topology.- 2.2 Continuous mappings.- 2.3 Wadge's hierarchy.- 2.4 Joint topologies on X* ? X?.- 3. The Chomsky hierarchy of ?-languages.- 3.1 Acceptance of ?-languages by automata.- 3.2 Finite automata and regular ?-languages.- 3.3 Context-free ?-languages.- 3.4 ?-languages accepted by Turing machines.- 4. Languages and ?-languages.- 4.1 ?-Kleene closure.- 4.2 ?-power languages.- 4.3 ?-transducers, gsm-mappings, and ?-transductions.- 4.4 Limit-closure.- 5. Wagner's hierarchy.- 5.1 Wagner classes.- 5.2 gsm-reducibility.- References.- 7. Languag...