Indexed language

Abstract: The 80 revised papers presented together with two keynote contributions and four invited papers were carefully reviewed and sele... The study of formal languages and automata has proved to be a source of much interest and discussion amongst mathematicians in recent times. This book, written by Professor Ian Chiswell, attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest i...

Abstract: A new type of grammar for generating formal languages, called an indexed grammar, is presented. An indexed grammar is an extension of a context-free grammar, and the class of languages generated by indexed grammars has closure properties and decidability results similar to those for context-free languages. The class of languages generated by indexed grammars properly includes all context-free languages and is a proper subset of the class of context-sensitive languages. Several subclasses of indexed grammars generate interesting classes of languages.

Abstract: Since the late 1970s there has been vigorous activity in constructing highly constrained grammatical systems by eliminating the transformational component either totally or partially. There is increasing recognition of the fact that the entire range of dependencies that transformational grammars in their various incarnations have tried to account for can be captured satisfactorily by classes of rules that are nontransformational and at the same time highly constrained in terms of the classes of grammars and languages they define. Two types of dependencies are especially important: subcategorization and filler-gap dependencies. Moreover, these dependencies can be unbounded. One of the motivations for transformations was to account for unbounded dependencies. The so-called nontransformational grammars account for the unbounded dependencies in different ways. In a tree adjoining grammar (TAG) unboundedness is achieved by factoring the dependencies and recursion in a novel and linguistically interesting manner. All dependencies are defined on a finite set of basic structures (trees), which are bounded. Unboundedness is then a corollary of a particular composition operation called adjoining . There are thus no unbounded dependencies in a sense. This factoring of recursion and dependencies is in contrast to transformational grammars (TG), where recursion is defined in the base and the transformations essentially carry out the checking of the dependencies. The phrase linking grammars (PLGs) (Peters and Ritchie, 1982) and the lexical functional grammars (LFGs) (Kaplan and Bresnan, 1983) share this aspect of TGs; that is, recursion builds up a set a structures, some of which are then filtered out by transformations in a TG, by the constraints on linking in a PLG, and by the constraints introduced via the functional structures in an LFG.

Abstract: Preface. Part A. Set Theory. 1. Basic Concepts of Set Theory. 2. Relations and Functions. 3. Properties of Relations. 4. Infinities. Appendix A1. Part B. Logic and Formal Systems. 5. Basic Concepts of Logic. 6.Statement Logic. 7. Predicate Logic. 8. Formal Systems, Axiomatization, and Model Theory. Appendix B1. Appendix BII. Part C. Algebra. 9. Basic Concepts of Algebra. 10. Operational Structures. 11. Lattices. 12. Boolean and Heyting Algebras. Part D. English as a Formal Language. 13. Basic Concepts of Formal Languages. 14. Generalized Quantifiers. 15. Intensionality. Part E. Languages, Grammars, and Automata. 16. Basic Concepts of Languages, Grammars, and Automata. 17. Finite Automata, Regular Languages and Type 3 Grammars. 18. Pushdown Automata, Context-Free Grammars and Languages. 19. Turing Machines, Recursively Enumberable Languages, and Type 0 Grammars. 20. Linear Bounded Automata, Context-Sensitive Languages and Type 1 Grammars. 21. Languages Between Context-Free and Context-Sensitive. 22. Transformational Grammars. Appendix EI. Appendix EII. Review Problems. Index.