Open AccessJournal Article
The boolean closure of growing context-sensitive languages
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TLDR
It is shown that there exists an infinite intersection hierarchy of GCSL and its deterministic counterpart called Church-Rosser Languages and the expressive power of the boolean closures of this class under the boolean operations is compared.Abstract:
The class of growing context-sensitive languages (GCSL) is a naturally defined subclass of context-sensitive languages whose membership problem is solvable in polynomial time. GCSL and its deterministic counterpart called Church-Rosser Languages (CRL) complement the Chomsky hierarchy in a natural way [9]. In this paper, the extension of GCSL obtained by closures of this class under the boolean operations are investigated. We show that there exists an infinite intersection hierarchy, answering an open problem from [1]. Further, we compare the expressive power of the boolean closures of GCSL, CRL, CFL and LOGCFL.read more
Citations
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References
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An Introduction to Kolmogorov Complexity and Its Applications
Ming Li,Paul M. B. Vitányi +1 more
TL;DR: The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics.
Journal ArticleDOI
Book Review: An introduction to Kolmogorov Complexity and its Applications Second Edition, 1997 by Ming Li and Paul Vitanyi (Springer (Graduate Text Series))
TL;DR: The complexity of a string is defined as the shortest description of x, and a formal definition is given that is equivalent to the one in the book.
Journal ArticleDOI
Two applications of inductive counting for complementation problems
TL;DR: It is shown that small numbers of “role switches” in two- person pebbling can be eliminated and a general result that shows closure under complementation of classes defined by semi-unbounded fan-in circuits is shown.
Journal ArticleDOI
Church-Rosser Thue systems and formal languages
TL;DR: Three ways in which formal languages can be defined by Thue systems with the Church-Rosser property are studied, and some general results about the three families of languages so determined are studied.
Journal ArticleDOI
Boolean grammars
TL;DR: In this paper, a new generalization of context-free grammars is introduced: Boolean Grammars, which allow the use of all set-theoretic operations as an integral part of the formalism of rules.