On omega-Sets Associated with Context-Free Languages

New families of ω-languages (sets of infinite sequences) associated with context-free languages and pushdown automata are introduced. Their basic properties, such as inclusion relations, closure under the Boolean operations and periodicity, are studied and compared with the corresponding properties of the families of ω-languages accepted by finite automata. Moreover, a number of solvability and unsolvability results are proved. The results obtained imply that there is a definite difference between the family of ω-languages accepted by pushdown automata and the family associated with context-free languages.