Indexed language

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

Contextual Grammars with Subregular Choice

Abstract: We discuss external contextual grammars with choice where the choice language belongs to a family of subregular languages. We determine the hierarchy of language families of contextual languages which is obtained by the use of nilpotent, combinational, definite, regular suffix closed, and regular commutative languages as choice languages.

Harmonic Grammars for Formal Languages

Abstract: Basic connectionist principles imply that grammars should take the form of systems of parallel soft constraints defining an optimization problem the solutions to which are the well-formed structures in the language. Such Harmonic Grammars have been successfully applied to a number of problems in the theory of natural languages. Here it is shown that formal languages too can be specified by Harmonic Grammars, rather than by conventional serial rewrite rule systems.

Groups with context-free conjugacy problems

Abstract: The conjugacy problem and the inverse conjugacy problem of a finitely generated group are defined, from a language theoretic point of view, as sets of pairs of words. An automaton might be obliged to read the two input words synchronously, or could have the option to read asynchronously. Hence each class of languages gives rise to four classes of groups; groups whose (inverse) conjugacy problem is an (a)synchronous language in the given class. For regular languages all these classes are identical with the class of finite groups. We show that the finitely generated groups with asynchronously context-free inverse conjugacy problem are precisely the virtually free groups. Moreover, the other three classes arising from context-free languages are shown all to coincide with the class of virtually cyclic groups, which is precisely the class of groups with synchronously one-counter (inverse) conjugacy problem. It is also proved that, for a δ-hyperbolic group and any λ ≥ 1, ϵ ≥ 0, the intersection of the inverse conjugacy problem with the set of pairs of (λ, ϵ)-quasigeodesics is context-free. Finally we show that the conjugacy problem of a virtually free group is an asynchronously indexed language.

A grammatical characterization of exponential-time languages

Abstract: We show that the languages generated by a constrained form of Chomsky's transformational grammars characterize the languages recognized by Turing machines in deterministic exponential (2cn) time. The constraints on the transformational grammars are satisfied by many, though not all, known grammars in linguistic practice. We also give a simple algebraic characterization of the same class of languages and use it for the linguistic characterization.

On context-free and Szilard languages

Abstract: Szilard languages of context-free grammars are studied. Especially, classical pumping, generalized pumping, Sokolowski's criterion, and semilinearity are considered as possible distinguishing properties between context-free and Szilard languages.