LR(k)-colored grammar and its application

Abstract

We introduce a new grammar called LR(k) colored grammar in which every grammar symbol and production rule of a context-free grammar G is colored by the information derived from the LR(k) parser for G. By using the grammar, we develop two results on the theory of grammars and parsing. First, we show that every LR(k) grammar can be covered by an SLR(k) gtammar (thus an LALR(K) grammar), which is known to be parsed more easily than LR(k) grammars. This new covering result for LR(k) grammars is obtained by showing that a context-free grammar G is covered by the LR (k)-colored grammar for G and that G is LR(k) if and only if the grammar is SLR(k). In addition, a natural reduction of the garammar which preserves the SLR(k) covering property is also developed. Second, 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 garmmars and some ambiguous grammars. A context-free grammar is said to be BLRC(k) if the number of conflict occurrenecs during LR(k) parsing for every sentence of the grammar is inherently bonded. A BLRC(k) grammar can be considered as a natrual 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 contextfree grammar is BLRC(k) for a given k. But it is undecidable for arbitrary k. The result is obtained by deriving another grammar called LR (k)-context description grammar from the LR(k)-clolred grammar as a tool for describing the behavior of given LR(k) parser in terms of the grammar symbols.