UNSOLVABILITY LEVELS OF OPERATION PROBLEMS FOR SUBCLASSES OF CONTEXT-FREE LANGUAGES
Henning Bordihn, Markus Holzer, Martin Kutrib · International Journal of Foundations of Computer Science · 2005
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.