Regulated rewriting in formal language theory
Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2008.
Context-free grammars are well-studied and well-behaved in terms of decidability, but many real-world problems cannot be described with context-free grammars. Grammars with regulated rewriting are grammars with mechanisms to regulate the applications of rules, so that certain derivations are avoided. Thus, with context-free rules and regulated rewriting mechanisms, one can often generate languages that are not context-free. In this thesis we study grammars with regulated rewriting mechanisms. We consider problems in which context-free grammars are insufficient and in which more descriptive grammars are required. We compare bag context grammars with other well-known classes of grammars with regulated rewriting mechanisms. We also discuss the relation between bag context grammars and recognizing devices such as counter automata and Petri net automata. We show that regular bag context grammars can generate any recursively enumerable language. We reformulate the pumping lemma for random permitting context languages with context-free rules, as introduced by Ewert and Van der Walt, by using the concept of a string homomorphism. We conclude the thesis with decidability and complexity properties of grammars with regulated rewriting.