Showing papers on "Chomsky hierarchy published in 1995"

Towards a mathematical theory of machine discovery from facts

Abstract: This paper intends to give a theoretical foundation of machine discovery from facts. We point out that the essence of a computational logic of scientific discovery or a logic of machine discovery is the refutability of the entire spaces of hypotheses. We discuss this issue in the framework of inductive inference of length-bounded elementary formal systems (EFSs), which are a kind of logic programs over strings of characters and correspond to context-sensitive grammars in Chomsky hierarchy. First we present some characterization theorems on inductive inference machines that can refute hypothesis spaces. Then we show differences between our inductive inference and some other related inferences such as in the criteria of reliable identification, finite identification and identification in the limit. Finally we show that for any n , the class, i.e. hypothesis space, of length-bounded EFSs with at most n axioms is inferable in our sense, that is, the class is refutable by a consistently working inductive inference machine. This means that sufficiently large hypothesis spaces are identifiable and refutable.

Automata That Take Advice

Abstract: Karp and Lipton introduced advice-taking Turing machines to capture nonuniform complexity classes. We study this concept for automata-like models and compare it to other nonuniform models studied in connection with formal languages in the literature. Based on this we obtain complete separations of the classes of the Chomsky hierarchy relative to advices.

A New Approach to Formal Language Theory by Kolmogorov Complexity

Abstract: We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic context-free languages and nondeterministic context-free languages. The use of the new "incompressibility arguments" is illustrated by many examples. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity.

Formal Languages and Infinite Groups

Abstract: This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.

Distributed Catenation and Chomsky Hierarchy

Abstract: We introduce a new operation between words and languages, called distributed catenation. The distributed catenation is a natural extension of the well known catenation operation from the theory of formal languages. As for partial shuffle operation the introduction of this operation is strongly motivated by the theory of concurrency. At the same time the distributed catenation is a powerful operation. For instance, any Turing machine can be simulated by a pushdown automaton that uses distributed catenation for the pushdown memory.

Evolution of Transformational Grammar

Abstract: Publisher Summary This chapter focuses on the evolution of transformational grammar It was developed in the mid-1950s by Noam Chomsky Over the next two decades it became the dominant paradigm in syntactic theory and description and its descendant, government binding theory, is still one of the most influential current theories Transformational grammar forms a wide-ranging theory, whose central tenets are the use of hypothetico-deductive methodology to construct formal models of certain aspects of human linguistic capabilities Such models are called “grammars” in the theory and are taken to be an encoding, in some form, of the native speaker's linguistic knowledge Structural linguistics is expected to transcend the limits of the sentence and offer a method of approaching discourse level structures For Chomsky, on the other hand, transformations formed part of a program directed at characterizing the nature and properties of the human language faculty Chomsky's analysis thus depends upon an abstract structure in which the affixes of the auxiliary system do not appear in their “surface” order

Indexed Languages and Unification Grammars

Abstract: Indexed languages are interesting in computational linguistics because they are the least class of languages in the Chomsky hierarchy that has not been shown not to be adequate to describe the string set of natural language sentences. We here define a class of unification grammars that exactly describe the class of indexed languages.

On properties of edtol and rwdol languages and the constructibility of finite morphic refinements

Abstract: In [5], it was shown that every regular language R and its complement is refined by a finite partition of A induced by a morphic (or equivalently fully invariant) congruence relation. More importantly, this refinement can be effectively constructed given a finite-state representation of R. In section two of this paper, it's shown that with respect to the standard Chomsky Hierarchy of Languages, the regular languages are unique in having the aforementioned property. Based on the result obtained in section two, the remainder of this work focuses on obtaining decidability results for classes of languages generated by intersecting regular languages with languages generated by two specific types of L-systems. In section three of this paper, given an EDTOL scheme a nd a regular language, the set of strings in A* such that the EDTOL language of w intersected with the given regular language is empty is a constructible regular language. Thus in particular, the problems of emptiness and containment in a regular set...