Some Non-semi-decidability Problems for Linear and Deterministic Context-Free Languages
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 .
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- 4.Bordihn, H.: Context-freeness of the power of context-free languages is undecidable. Theoretical Computer Science (2003) (to appear)Google Scholar
- 6.Calbrix, H., Nivat, M.: Prefix and period languages and rational ω-languages. In: Developments in Language Theory II. At the Crossroads of Mathematics, Computer Science and Biology, pp. 341–349. World Scientific, Singapore (1996)Google Scholar
- 12.Hartmanis, J.: Context-free languages and Turing machine computations. In: Proceedings of Symposia in Applied Mathematics, vol. 19. American Mathematical Society, Providence (1967)Google Scholar