An overview of conjunctive grammars

AbstractConjunctive grammars were introduced in 2000 as a generalization ofcontext-free grammars that allows the use of an explicit intersection oper-ation in rules. Several theoretical results on their properties have been ob-tained since then, and a number of efficient parsing algorith ms that justifythe practical value of the concept have been developed. This article reviewsthese results and proposes numerous open problems. 1 Introduction The generative power of context-free grammars is generallyconsidered to beinsufficient for denoting many languages that arise in pract ice: it has often beenobserved that all natural languages contain non-context-free constructs, whilethe non-context-freeness of programming languages was proved already in early1960s. A review of several widely different subject areas led the authors of [5] tothe noteworthy conclusion that “the world seems to be non-context-free”.This leaves the aforementioned world with the question of fin ding an ade-quate tool for denoting formal languages. As the descriptive means of context-free grammars are not sufficient but necessary for practical use, the attemptsat developing new generative devices have usually been made by generalizingcontext-free grammars in this or that way. However, most of the time an exten-sion that appears to be minorleads to a substantialincrease in the generative power(context-sensitive and indexed grammars being good examples), which is usuallyaccompanied by strong and very undesirable complexity hardness results. Theability to encode hard problems makes a formalism, in effect, a peculiar low-levelprogramming language, where writing a grammar resembles coding in assembly