BOUNDEDLY LR(K)-CONFLICTABLE GRAMMARS

Abstract

We present a new class of context-free grammars whose sentences are parsable in linear time and space. The class called boundedly LR(k)-conflictable (BLRC(k)) grammars includes all LR(k) grammars, some non-LR unambiguous grammars and some boundedly ambiguous grammars. A context-free grammar is said to be BLRC(k) if the number of conflict occurences during LR(k) parsing for every sentence of the grammar is inherently bounded. A BLRC(k) grammar can be considered as a natural extension of an LR(k) grammar whose sentences can be parsed by an LR(k) manner with multiple stacks. We show that it is a decidable problem whether a context-free grammar is BLRC(k) for a given k, whereas it is undecidable for arbitrary k. The result is derived from an LR (k) machine description grammar which describes the behavior of a given LR(k) parser in terms of the grammar symbols. The relationship between the class of BLRC(k) grammars (and languages) and those of other associated grammars (and languages), is also discussed.