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.

Contributions to the theory of finite-state based grammars

Abstract: This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIGs) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchy and the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, leftand right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the ChomskySchutzenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance motivated approximations are linear-time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as the generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing.

The Chop of Languages.

Abstract: We investigate chop operations, which can be seen as generalized concatenation. For several language families of the Chomsky hierarchy we prove (non)closure properties under chop operations and incomparability to the family of languages that are the chop of two regular languages. We also prove non-closure of that language family under Boolean operations and closure under reversal. Further, the representation of a regular language as the chop of two regular expressions can be exponentially more succinct than its regular expression. By considering the chop of two linear context-free languages we already obtain language families that have non-semi-decidable problems such as emptiness or finiteness.

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.

Language families defined by a ciliate bio-operation: hierarchies and decision problems

Abstract: We formalize the hairpin inverted repeat excision, which is known in ciliate genetics as an operation on words and languages by defining as the set of all words xαyRαRz where w = xαyαRz and the pointer α is in P. We extend this concept to language families which results in families . For and be the families of finite, regular, context-free, context-sensitive or recursively enumerable language, respectively, we determine the hierarchy of the families and compare these families with those of the Chomsky hierarchy. Furthermore, we present the status of decidability of the membership problem, emptiness problem and finiteness problem for the families .