Epsilon Precedence Grammars and Languages

The classes of simple and weak precedence grammars are generalized to include ε-rules (productions with the empty right parts). The descriptive power of epsilon simple precedence (ESP) grammars increases directly with the number of ε-rules permitted; the class of ESP grammars with no ε-rules, ESP0, is identical to the class of simple precedence grammars; ESP grammars with at most one ε-rule, ESP1, define a class of languages which properly includes the class of ESP0 languages, but is itself properly included in the class of deterministic, context-free languages. In general, ESP grammars having at most i ε-rules, ESPi, define a class of languages which is properly included in that defined by ESPi+1 grammars. This hierarchy of languages exhausts the deterministic context-free languages. The hierarchy of ESP languages is established using an iteration theorem which may be used to show that a given language is not ESPi for a given i. An algorithm to convert arbitrary LR(1) grammars to equivalent epsilon weak precedence (EWP) grammars is developed. The class of Viable Prefix EWP grammars is defined and it is shown that the EWP parser for every Viable Prefix EWP grammar detects syntactic errors at the earliest possible time. Also, it is established that every deterministic context-free language is defined by some Viable Prefix EWP grammar. Finally, it is shown that the class of EWP grammars, while properly containing the class of Viable Prefix EWP grammars, is itself properly included in the well-known classes of context-free grammars with the ε-rules which define exactly the deterministic context-free languages

Context-Free Grammars: Covers, Normal Forms, and Parsing

This monograph develops a theory of grammatical covers, normal forms and parsing. Covers, formally defined in 1969, describe a relation between the sets of parses of two context-free grammars. If this relation exists then in a formal model of parsing it is possible to have, except for the output, for both grammars the same parser. Questions concerning the possibility to cover a certain grammar with grammars that conform to some requirements on the productions or the derivations will be raised and answered. Answers to these cover problems will be obtained by introducing algorithms that describe a transformation of an input grammar into an output grammar which satisfies the requirements. The main emphasis in this monograph is on transformations of context-free grammars to context-free grammars in some normal form. However, not only transformations of this kind will be discussed, but also transformations which yield grammars which have useful parsing properties