Rewriting Systems with Restricted Configurations

#-rewriting system, configuration, descriptional complexity, determinism, dynamic complexity, finite index, formal model, generative power, language, language family, n-limitation, m-parallel n-right-linear simple matrix grammar, programmed grammar, restricted pushdown automaton, reducing deep pushdown automaton, regulated rewriting system, restriction, state grammar

This theoretically oriented dissertation discusses rewriting systems, including various automata and grammars.  It concentrates its attention upon their combination.  More specifically, the central role of the present dissertation plays the general notion of a configuration as an instantaneous description of a rewriting system.  Based upon various restrictions placed upon configurations and rewriting modes, the systems are classified and studied. Apart from this major topic, the dissertation also discusses dynamic complexity, which is based upon metrics placed upon the process of yielding strings.     As its fundamental topic, the dissertation discusses #-rewriting system,  reducing deep pushdown automaton, and pushdown automata with restricted pushdowns. In addition, it studies some variants of #-rewriting systems, including n-right linear and generalized #-rewriting system.  In general, the dissertation demonstrates how the generative power of the systems under discussion depends upon the restrictions placed upon them. In terms of dynamic complexity, it discusses a close relationship between various rewriting systems, including newly introduced systems.  As its main result, the dissertation demonstrates several infinite hierarchies of language families defined by rewriting systems in dependency on their restrictions.          The conclusion demonstrates the application-important properties of the systems discussed in the dissertation. It sketches two new types of determinism and canonical rewriting; then, it demonstrates their potential practical usage.