Chapter 13 Regulated Multigenerative Grammar Systems

Abstract

This two-section chapter discusses regulated versions of grammar systems, referred to as multigenerative grammar systems, which consist of several components represented by context-free grammars. Their regulation is based upon a simultaneous generation of several strings, which are composed together by some basic operation, such as concatenation, after their generation is completed. Section 13.1 defines the basic versions of multigenerative grammar systems. During one generation step, each of their grammatical components rewrites a nonterminal in its sentential form. After this simultaneous generation is completed, all the generated strings are composed into a single string by some common string operation, such as union and concatenation. It is shown that these systems characterize the family of matrix languages. In addition, the section demonstrates that multigenerative grammar systems with any number of grammatical components can be transformed to equivalent two-component versions of these systems. Section 13.2 discusses leftmost versions of multigenerative grammar systems in which each generation step is performed in a leftmost manner. That is, all the grammatical components of these versions rewrite the leftmost nonterminal occurrence in their sentential forms; otherwise, they work as the basic versions. This section proves that leftmost multigenerative grammar systems are more powerful than their basic versions because they are computationally complete. It demonstrates that leftmost multigenerative grammar systems with any number of grammatical components can be transformed to equivalent two-component versions of these systems.