Showing papers on "Chomsky hierarchy published in 2014"

Linguistic models at the crossroads of agents, learning and formal languages

Abstract: This paper aims at reviewing the most relevant linguistic applications developed in the intersection between three different fields: machine learning, formal language theory and agent technologies. On the one hand, we present some of the main linguistic contributions of the intersection between machine learning and formal languages, which constitutes a well-established research area known as Grammatical Inference. On the other hand, we present an overview of the main linguistic applications of models developed in the intersection between agent technologies and formal languages, such as colonies, grammar systems and eco-grammar systems. Our goal is to show how interdisciplinary research between these three fields can contribute to better understand how natural language is acquired and processed.

Discovering the discovery of the hierarchy of formal languages

Abstract: The hierarchy of formal languages is a mathematical representation of linguistic geometry (LG). LG is a type of game theory for a class of extensive discrete games called abstract board games (ABG), scalable to the level of real life defense systems. LG is a formal model of human reasoning about armed conflict, a mental reality “hard-wired” in the human brain. LG, an evolutionary product of millions of years of human warfare, must be a component of the primary language of the human brain (as introduced by Von Neumann). Experiences of development of LG must be instructive for solving another major puzzle, discovering the algorithm of discovery, yet another ancient component of the primary language. This paper reports results on discovering mental processes involved in the development of the hierarchy of formal languages. Those mental processes manifesting execution of the algorithm of discovery are called visual streams. This paper reveals the visual streams that were involved in the thought experiments led to the development of the formal theory of LG. Specifically, it demonstrates the streams involved in choosing the formal-linguistic representation of LG; the type of formal languages and grammars, the so-called controlled grammars; the construction of the grammars of shortest trajectories and the grammar of zones. This paper introduces a hypothesis of how we construct and focus visual streams.

Towards a Coalgebraic Chomsky Hierarchy

Abstract: The Chomsky hierarchy plays a prominent role in the foundations of theoretical computer science relating classes of formal languages of primary importance. In this paper we use recent developments on coalgebraic and monad-based semantics to obtain a generic notion of a \(\mathbb{T}\)-automaton, where \(\mathbb{T}\) is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for \(\mathbb{T}\)-automata, and we show by numerous examples that it correctly instantiates for some known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for studying expressivity power of various machine-based models.

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.

Computational complexity in the brain.

Abstract: How complex is human language? Every chapter in this volume is devoted, in one way or another, to addressing this question. The great majority of the chapters focus on the question of whether languages can be compared in terms of their relative degree of complexity. The present chapter, however (along with the one by Trotzke and Zwart) takes a somewhat different approach to the question of grammatical complexity. We ask: ‘How might one characterize the degree of complexity of natural language in general?’ Fortunately there are formal means of measuring the complexity of grammatical systems that go back to the 1950s. We refer, of course, to the Chomsky hierarchy (Chomsky 1956, 1963), which classes grammars, and the automata that recognize them, in formal terms. Our chapter goes beyond that of Trotzke and Zwart, however, in attempting to identify the brain activity that correlates with the formally-arrived at levels of grammar in the hierarchy. We will see that the relationship between the hierarchy and both measurable processing difficulty and detectable brain activity is not a simple one. The chapter is organized as follows. Section 2 reviews briefly the Chomsky hierarchy. Section 3 investigates the processing (primarily parsing) correlates of the hierarchy and §4 the neurophysiological correlates. Section 5 further probes the modeling by automata of neurolinguistics processes. Section 6 is a brief conclusion.

The Non-Hierarchical Nature of the Chomsky Hierarchy-Driven Artificial-Grammar Learning

Abstract: Recent artificial-grammar learning (AGL) paradigms driven by the Chomsky hierarchy paved the way for direct comparisons between humans and animals in the learning of center embedding ([A[AB]B]). The AnBn grammars used by the first generation of such research lacked a crucial property of center embedding, where the pairs of elements are explicitly matched ([A1 [A2 B2] B1]). This type of indexing is implemented in the second-generation AnBn grammars. This paper reviews recent studies using such grammars. Against the premises of these studies, we argue that even those newer AnBn grammars cannot test the learning of syntactic hierarchy. These studies nonetheless provide detailed information about the conditions under which human adults can learn an AnBn grammar with indexing. This knowledge serves to interpret recent animal studies, which make surprising claims about animals’ ability to handle center embedding.

Towards a Coalgebraic Chomsky Hierarchy

Abstract: The Chomsky hierarchy plays a prominent role in the foundations of the theoretical computer science relating classes of formal languages of primary importance. In this paper we use recent developments on coalgebraic and monad-based semantics to obtain a generic notion of a $\mathbb{T}$-automaton, where $\mathbb{T}$ is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, valence automata, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for $\mathbb{T}$-automata, and we show by numerous examples that it correctly instantiates for the known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for proving expressivity bounds of various machine-based models.

Unification and Efficient Computation in the Minimalist Program

Abstract: This talk explores issues in the construction of computationally simple grammars. In particular, we investigate the trade-off between simplicity of implementation and expressive power. We begin by developing what appears to be the simplest possible definite clause grammar implementation for a sub-theory in the minimalist program: that of probe-goal case agreement (Chomsky, Lectures in Government and Binding. Dordrecht: Foris; 2001). In computational modeling, there is a simple trade-off between simplicity of mechanism and expressive power, e.g., the Chomsky hierarchy. However, simplicity of implementation need not correlate with limited expressive power. Unification is a simple but powerful mechanism that can be used to implement uninterpretable/interpretable feature matching. We show, using examples from Chomsky (Lectures in Government and Binding. Dordrecht: Foris; 2001), as in (1)–(3), that unification-based derivations result in agree relations with fewer probe-goal steps than predicted. This economy of derivation results because once unified, unvalued features from different heads can be instantiated or valued simultaneously at a parse global level. Therefore, unification trades off fewer probe-goal steps for possibly unbounded agree relations.

The generative power of weighted one-sided and regular sticker systems

Abstract: Sticker systems were introduced in 1998 as one of the DNA computing models by using the recombination behavior of DNA molecules. The Watson-Crick complementary principle of DNA molecules is abstractly used in the sticker systems to perform the computation of sticker systems. In this paper, the generative power of weighted one-sided sticker systems and weighted regular sticker systems are investigated. Moreover, the relationship of the families of languages generated by these two variants of sticker systems to the Chomsky hierarchy is also presented.

Restarting Automata for Picture Languages: A Survey on Recent Developments

Abstract: Much work has been done to obtain classes of picture languages that would correspond to the classes of the Chomsky hierarchy for string languages, and finally the class REC of recognizable picture languages has been agreed on as the class that corresponds to the ‘regular string languages.’ This class has several nice characterizations in terms of regular expressions, tiling automata, and on-line tesselation automata, and it has nice closure properties, but it also has two main drawbacks: all its characterizations are highly nondeterministic in nature, and it contains languages that are NP-complete. Consequentially, various deterministic subclasses of REC have been defined. Mainly, however, these definitions are quite complex, and it is not clear which of the resulting classes should be considered as ‘the’ class of deterministic recognizable picture languages. Here we present some recent developments obtained in a research project that aims at finding a deterministic model of a two-dimensional automaton that has the following desirable properties:

An Outline of the Development of the Theory of Formal languages

Abstract: The objective of this paper is to present a crisp and critical survey of the development of the theory of formal languages. It is known that the study of formal languages was initiated in order to give a precise characterization of the structure of natural languages with the goal of defining its syntax using simple and precise mathematical rules. The mathematical theory of formal languages grew with the need of formalizing and describing the process linked with the use of computers and communication devices. In course of time, it has occupied an important place in the core of education of computer scientists and linguists, and more recently, it has found applications as well in soft sciences, such as, biology and economics.

Representation of regular formal languages.

Abstract: This dissertation presents three different approaches to representing Regular Formal languages, i.e., regular expressions, finite acceptors and regular grammars. We define how each method is used to represent the language, and then the method for translating from one representation to another of the language. A toolkit is then presented which allows the user to input their definition of a language using any of the three models, and also allows the user to translate the representation of the language from one model to another.

Chomsky : language, mind, politics

Abstract: Preface vi Introduction 1 1 Chomsky s Contributions 7 2 The Mind and Its Sciences 26 3 Partitioning the Mind: Bad and Good Cognitive Science 52 4 Human Problem-Solving Capacities 69 5 The Science of Language 89 6 Linguistic Meanings and Their Uses 136 7 Chomsky on Politics: Some Basic Themes 158 8 Language and Politics: Justification 205 Glossary 234 Notes 238 Bibliography 245 Index 254

Survey of Bounding Theory in Arabic Language

Abstract: Government and Binding Theory or Principles and Parameters Theory is a universal theory of Chomsky. Linguists of world believe that Chomsky made a revolution in linguistics by this theory. One of the sub-theories of Government and Binding Theory is Bounding Theory which explains the restrictions of grammatical movements. Chomsky claims that his theory is universal and you can perform it in all languages. This essay considers this sub-theory (Bounding Theory) in Arabic language whether is performable in this language. If the answer is positive which grounds movement include off? Some of the movement restrictions of Arabic language are like the other languages, but some of the restrictions and movements are more than what is said in this subtheory by Chomsky.