Some non-semi-decidability problems for linear and deterministic context-free languages

Authors:
Henning Bordihn;Markus Holzer;Martin Kutrib
Affiliations:
Institut für Informatik, Universität Potsdam, Potsdam, Germany;Institut für Informatik, Technische Universität München, Garching bei München, Germany;Institut für Informatik, Universität Giessen, Giessen, Germany
Venue:
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Year:
2004

Citing 12
Cited 2

Formal languages

Formal languages
Some Recursively Unsolvable Problems in ALGOL-Like Languages

Journal of the ACM (JACM)
The Unsolvability of the Recognition of Linear Context-Free Languages

Journal of the ACM (JACM)
Parenthesis Grammars

Journal of the ACM (JACM)
A Generalization of Ogden's Lemma

Journal of the ACM (JACM)
L(A) = L(B)? decidability results from complete formal systems

Theoretical Computer Science
Theory of Computation: A Primer

Theory of Computation: A Primer
Introduction To Automata Theory, Languages, And Computation

Introduction To Automata Theory, Languages, And Computation
The Power of One-Letter Rational Languages

DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Context-freeness of the power of context-free languages is undecidable

Theoretical Computer Science
Reversal-bounded multipushdown machines

Journal of Computer and System Sciences
Roots and powers of regular languages

DLT'02 Proceedings of the 6th international conference on Developments in language theory

Splittability of bilexical context-free grammars is undecidable

Computational Linguistics
The boolean closure of linear context-free languages

DLT'04 Proceedings of the 8th international conference on Developments in Language Theory

Quantified Score

Hi-index	0.00

Visualization

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 for all of the aforementioned operations, if the underlying alphabet contains at least two letters. The non-semi-decidability and thus the undecidability for the power operation solves an open problem stated in [4].