Completion grammars and completion automata revisited

An extension of completion grammars is being introduced such that the model now deals with prefix, infix, postfix and post-infix word order patterns. It is shown that this extension does not affect the weak generative capacity of the system, which was known to be of type 2. Also the existing notion of a completion automaton is reworked, mainly to have the distinction in word order be reflected by the operations of the automaton rather than by the transition functions of the underlying finite state machine. In some recent publications (e.g. Steels (1975), Steels and Vermeir (1976), Steels (1976ab1976a&b). What will concern us in this paper is an extension of the model, and a study of the formal properties of these extended systems. Also we will introduce a new class of automata. The paper is organized as follows. First we extend the notion of a completion grammar, we give some intuitive explanations for the extension (1.1.), specify the basic definitions (1.2.) and study its weak generative capacity (1.3.). A second section deals with the automata. Again we start with intuitive explanations (2.1.), give the basic definitions and various examples (2.2.) and finally prove the relation between the grammars and the automata (2.3.).