Indexed language

About: Indexed language is a research topic. Over the lifetime, 334 publications have been published within this topic receiving 11000 citations.

New frontiers beyond context-freeness: DI-grammars and DI-automata

Abstract: A new class of formal languages will be defined - the Distributed Index Languages (DI-languages). The grammar-formalism generating the new class - the DI-grammars - cover unbound dependencies in a rather natural way. The place of DI-languages in the Chomsky-hierarchy will be determined: Like Aho's indexed Languages, DI-languages represent a proper subclass of Type 1 (contextsensitive languages) and properly include Type 2 (context-free languages), but the DI-class is neither a subclass nor a superclass of Aho's indexed class. It will be shown that, apart from DI-grammars, DI-languages can equivalently be characterized by a special type of automata - DI-automata. Finally, the time complexity of the recognition-problem for an interesting subclass of DI-Grammars will approximately be determined.

The emptiness problem for indexed language is exponential‐time complete

Abstract: The class of indexed languages properly includes the class of context-free languages and is properly included in the class of context-dependent languages [1]. The emptiness problem (the problem of determining whether or not the given language is empty) is polynomial-time complete for the class of context-free languages and is undecidable for the class of context-dependent languages. The recognition problem (the problem, given a language L and word w, of determining whether or not w belongs to L) is polynomial-time complete for the class of context-free languages and is polynomialspace complete for the class of contextdependent languages. This paper shows that both the emptiness and recognition problems are exponential-time complete for the class of indexed languages. It is known in the pebble game [2] that the problem of determining whether or not the first player has the winning strategy is exponential-time complete. This paper reduces the problem to the emptiness problem for the class of indexed languages in the logarithmic space, indicating the exponential-time difficulty of the emptiness problem for the indexed language. Since Aho has shown that the problem can be answered in exponential time, the exponential-time completeness is shown. The exponential-time difficulty is also directly indicated from the fact that the emptiness problem is exponential-time complete. Consequently, the recognition problem is also exponential-time complete.

A generalizationnof the offline parsable grammars

Abstract: The offline parsable grammars apparently have enough formal power to describe human language, yet the parsing problem for these grammars is solvable. Unfortunately they exclude grammars that use x-bar theory - and these grammars have strong linguistic justification. We define a more general class of unification grammars, which admits x-bar grammars while preserving the desirable properties of offline parsable grammars.

k-gram extensions of terminal distinguishable languages

Abstract: We show how k-grams can be used to extend classes of terminal distinguishable right-liner languages (k-TDRL). Moreover, we present an efficient identification algorithm for k-TDRL languages. Our approach not only generalizes the class TDRL, but also the k-testable languages, as well as the k-reversible languages.

An overview of conjunctive grammars

Abstract: Conjunctive 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