Chomsky hierarchy

About: Chomsky hierarchy is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 31067 citations. The topic is also known as: Chomsky–Schützenberger hierarchy.

On Pregroups, Freedom, and (Virtual) Conceptual Necessity

Abstract: The advent of the Minimalist Program (Chomsky, 1995) heralded a shift of emphasis from the by now familiar goals of descriptive and explanatory adequacy, to a characterization of human language in terms of departures from a minimally necessary system meeting various boundary ('bare output') conditions. This involves determining both what the appropriate boundary conditions are, and what the simplest systems are that meet these conditions. Work within the minimalist program can be viewed as concerning itself primarily with the first question: the nature of the interfaces. Work in theoretical computational linguistics, on the other hand, is easily understood as seeking answers to the second. Viewing languages as sets of strings, although an obvious simplification, allows us to formulate precisely simple but interesting boundary conditions, which in turn enables feasible inquiry into the various possible formalisms which meet these boundary conditions. Perhaps the best studied such boundary condition is that the grammar formalism be able to describe a particular class £ of languages, where £ usually ranges over classes of languages as given by the Chomsky hierarchy (Chomsky, 1956), or various refinements thereof. 1 Results obtained here bear directly on the questions raised by Chomsky, as they can be understood as exhibiting the minimal properties a grammar formalism must have in order to be able to describe (as such) the complex of patterns attested in natural language. Properties of motivated linguistic formalisms can be compared against these minimal properties, and differences in complexity can either be interpreted as providing evidence for heretofore unacknowledged boundary conditions, or, if there is no structure in the deviations from minimality, as departures of our language faculty from perfection. There is a broad consensus that languages are usefully described in terms of a finite set of generators (the lexicon) which are acted upon by another finite

Improving the Accuracy of Large Vocabulary Continuous Speech Recognizer Using Dependency Parse Tree and Chomsky Hierarchy in Lattice Rescoring

Abstract: This research work describes our approaches in using dependency parse tree information to derive useful hidden word statistics to improve the baseline system of Malay large vocabulary automatic speech recognition system. The traditional approaches to train language model are mainly based on Chomsky hierarchy type 3 that approximates natural language as regular language. This approach ignores the characteristics of natural language. Our work attempted to overcome these limitations by extending the approach to consider Chomsky hierarchy type 1 and type 2. We extracted the dependency tree based lexical information and incorporate the information into the language model. The second pass lattice rescoring was performed to produce better hypotheses for Malay large vocabulary continuous speech recognition system. The absolute WER reduction was 2.2% and 3.8% for MASS and MASS-NEWS Corpus, respectively.

Grammars with bounded-life resources

Abstract: In the present paper we discuss a limitation of the resources activation (productions or nonterminals) of a Chomsky grammar. We associate a possible infinite natural number with each production/nonterminal of a grammar which restricts its possibility to participate arbitrarily many times in the string generation. This number may be viewed as the lifetime of that resource. We prove that this restriction does not lead to an increase in the computational power. A specific descriptional complexity criterion, namely the minimal number of immortal productions/nonterminals of a grammar and its extension to languages is investigated. Finally, we define grammars with bounded-frequency resources and prove that they are more powerful than grammars with bounded-life resources.

Complexity of Two-Dimensional Patterns

Abstract: In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a {\it language} or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of ``regular language'' or ``local rule'' that are equivalent in $d=1$ lead to distinct classes in $d \geq 2$. We explore the closure properties and computational complexity of these classes, including certain undecidability and {\bf NP}-completeness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in $d \geq 2$ has a periodic point of a given period, and that certain ``local lattice languages'' are not finite-time images or limit sets of any CA. We also show that the entropy of a $d$-dimensional CA's finite-time image cannot decrease faster than $t^{-d}$ unless it maps every initial condition to a single homogeneous state.

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.