UNSOLVABILITY LEVELS OF OPERATION PROBLEMS FOR SUBCLASSES OF CONTEXT-FREE LANGUAGES-Reference-Cited by-同舟云学术

UNSOLVABILITY LEVELS OF OPERATION PROBLEMS FOR SUBCLASSES OF CONTEXT-FREE LANGUAGES

Published:2005-06 Issue:03 Volume:16 Page:423-440
ISSN:0129-0541
Container-title:International Journal of Foundations of Computer Science
language:en
Short-container-title:Int. J. Found. Comput. Sci.

Author:

BORDIHN HENNING¹,HOLZER MARKUS²,KUTRIB MARTIN³

Affiliation:

1. Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, D-14482 Potsdam, Germany

2. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, D-85748 Garching bei München, Germany

3. Institut für Informatik, Universität Giessen, Arndtstraße 2, D-35392 Giessen, Germany

Abstract

We investigate the operation problem for linear and deterministic context-free languages: Fix an operation on formal languages. Given linear (deterministic, respectively) context-free languages, is the application of this operation to the given languages still a linear (deterministic, respectively) context-free language? Besides the classical operations, for which the linear and deterministic context-free languages are not closed, we also consider the recently introduced root and power operation. We show non-semi-decidability, to be more precise, we show completeness for the second level of the arithmetic hierarchy for all of the aforementioned operations, except for the power operation, if the underlying alphabet contains at least two letters. The result for the power operation solves an open problem stated in Theoret. Comput. Sci.314 (2004) 445–449.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129054105003078

Reference19 articles.

1. Reversal-bounded multipushdown machines

2. A Generalization of Ogden's Lemma

3. Context-freeness of the power of context-free languages is undecidable

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Non-Recursive Trade-Offs Are “Almost Everywhere”;Computing with Foresight and Industry;2019

2. Complexity of Operation Problems;Language, Life, Limits;2014

3. Decidability of operation problems for T0L languages and subclasses;Information and Computation;2011-03

4. Undecidability of Operation Problems for T0L Languages and Subclasses;Language and Automata Theory and Applications;2009

5. The Boolean closure of linear context-free languages;Acta Informatica;2008-01-10