Showing papers on "Chomsky hierarchy published in 2008"

Spiking neural P systems with extended rules: universality and languages

Abstract: We consider spiking neural P systems with rules allowed to introduce zero, one, or more spikes at the same time. The motivation comes both from constructing small universal systems and from generating strings; previous results from these areas are briefly recalled. Then, the computing power of the obtained systems is investigated, when considering them as number generating and as language generating devices. In the first case, a simpler proof of universality is obtained, while in the latter case we find characterizations of finite and recursively enumerable languages (without using any squeezing mechanism, as it was necessary in the case of standard rules). The relationships with regular languages are also investigated.

Syntactic Anchors: On Semantic Structuring

Abstract: 1. In defense of Deep-Structure 2. So what's in a Word? 3. Relational nouns, reference and grammatical relations 4. Online conditions and parametric variation 5. Prepositional case throughout 6. Iteration and related matters 7. (Re)interpreting the Chomsky hierarchy 8. Naturalizing meaning Epilogue: Evo-Devo-Perfo.

Representations and characterizations of languages in Chomsky hierarchy by means of insertion-deletion systems

Abstract: Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schutzenberger representation of context-free languages, i.e., in the form L = h(L(γ) ∩ D), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.

Efficient context-free grammar constraints

Abstract: With the introduction of constraints based on finite automata a new line of research has opened where constraints are based on formal languages. Recently, constraints based on grammars higher up in the Chomsky hierarchy were introduced. We devise a time- and space-efficient incremental arc-consistency algorithm for context-free grammars. Particularly, we show how to filter a sequence of monotonically tightening problems in cubic time and quadratic space. Experiments on a scheduling problem show orders of magnitude improvements in time and space consumption.

The algebraic approach I: the algebraization of the chomsky hierarchy

Abstract: The algebraic approach to formal language and automata theory is a continuation of the earliest traditions in these fields which had sought to represent languages, translations and other computations as expressions (eg regular expressions) in suitably-defined algebras; and grammars, automata and transitions as relational and equational systems over these algebras, that have such expressions as their solutions The possibility of a comprehensive foundation cast in this form, following such results as the algebraic reformulation of the Parikh Theorem, has been recognized by the Applications of Kleene Algebra (AKA) conference from the time of its inception in 2001 Here, we take another step in this direction by embodying the Chomsky hierarchy, itself, within an infinite complete lattice of algebras that ranges from dioids to quantales, and includes many of the forms of Kleene algebras that have been considered in the literature A notable feature of this development is the generalization of the Chomsky hierarchy, including type 1 languages, to arbitrary monoids

Duplication in DNA Sequences

Abstract: Duplication and repeat-deletion are the basic models of errors occurring during DNA replication from the viewpoint of formal languages. During DNA replication, subsequences of a strand of DNA may be copied several times (duplication) or skipped (repeat-deletion). Iterated duplication and repeat-deletion have been well-studied, but little is known about single-step duplication and repeat-deletion. In this paper, we investigate properties of these operations, such as closure properties of language families in the Chomsky hierarchy, language equations involving these operations. We also make progress towards a characterization of regular languages that are generated by duplicating a regular language.

The algebraic approach II: dioids, quantales and monads

Abstract: The algebraic approach to formal language and automata theory is a continuation of the earliest traditions in these fields which had sought to represent languages, translations and other computations as expressions (e.g. regular expressions) in suitably-defined algebras; and grammars, automata and transitions as relational and equational systems over these algebras that have such expressions as their solutions. As part of a larger programme to algebraize the classical results of formal language and automata theory, we have recast and generalized the Chomsky hierarchy as a complete lattice of dioid algebras. Here, we will formulate a general construction by ideals that yields a family of adjunctions between the members of this hierarchy. In addition, we will briefly discuss the extension of the dioid hierarchy to semirings and power series algebras.

Desperately evolving syntax

Abstract: The Chomsky Hierarchy (CH) gives a first approximation as to where human syntax lies in an abstract logical space: the generating device accepting appropriate languages should be slightly more powerful than a standard Push-Down Automaton (a PDA+), although for familiar reasons not much more so. An evolutionary study of syntax ought to give us some clues as to how a PDA+ could have emerged in brains. The goal of my talk is to provide an approach to this question that is informed about contemporary considerations in the Eva-Devo paradigm and, especially, standard results in the study of syntax

Topological Complexity of Context-Free omega-Languages: A Survey

Abstract: We survey recent results on the topological complexity of context-free omega-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free omega-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of ambiguity, and the special case of omega-powers.

Explicit and Implicit Assumptions in Noam Chomsky’s Theory of Language

Abstract: The author identifi es selected implicit or not fully explicit assumptions made by Noam Chomsky in his theory of language. Through a careful examination of Chomsky’s work, she aims to present the solutions this linguist proposes with respect to two fundamental questions: the question of methodology and the question of the ontological status of language. After reviewing the central theses of Chomsky’s theory in the fi rst part of the paper, she turns to the question that is mentioned in the title of this paper, that is, the reservations regarding the assumptions underlying Chomsky’s work. I. Introductory Remarks The methodological assumptions as well as the preliminary answers that were introduced by Noam Chomsky as he was laying the foundations for 20c linguistics have long been considered a classic of refl ection on the basic problems in the philosophy of language. In particular, whenever the questions of language acquisition, language innateness or the methods for the study of language are raised, his theories are customarily quoted either as a starting point for further discussion or, at least, as a reference point for the author’s own views. Nevertheless, the classic status of Chomsky’s texts is no help in their study. Numerous comments, both by his supporters and opponents, together with the evolution of his standpoint make the task of clarifying the basic notions and sorting out his theses all the more diffi cult. Chomsky’s works and the problems addressed therein have been of signifi cant importance from the point of view of the philosophy of language, and the philosophical effort of putting Chomsky’s linguistic conception in FORUM PHILOSOPHICUM 13(2008), pp. 83-101 forum 13 wiosna.indd Sek6:85 2008-07-08 21:06:48

The Boolean Closure of Growing Context-Sensitive Languages

Abstract: The set of growing context-sensitive languages (GCSL) is a naturally defined subclass of context-sensitive languages whose membership problem is solvable in polynomial time. Moreover, growing context-sensitive languages and their deterministic counterpart called Church-Rosser Languages (CRL) complement the Chomsky hierarchy in a natural way [13]. In this paper, closures of GCSL under the boolean operations are investigated. It is shown that there exists an infinite intersection hierarchy for GCSL and CRL, answering an open problem from [2]. Furthermore, the expressive power of the boolean closures of GCSL, CRL, CFL and LOGCFL are compared.

La jerarquía de Chomsky y la facultad del lenguaje: consecuencias para la variación y la evolución *

Abstract: This paper explores the relevance of the so-called Chomsky Hierarchy (ChH) when studying I-language phenomena, reinterpreting it in terms of the operation Merge. It is argued that all ChH levels of complexity discussed in Chomsky (1956) (i.e., finite state, phrase structure, and transformations) are present in the Faculty of Language, with (possible) consequences for language variation. RESUMEN

Formal Grammars for early child language

Abstract: This thesis develops a formal grammar for the two-word stage, one the earliest stages in the development of Dutch child language acquisition. The validity of this grammar is evaluated against the relevant parts of the Childes corpus. Some less formal observations about the earliest multi-word stage (the stage following the two-word stage) are formulated.