@article{TAKAHASHI19751,
    Abstract = {We extend the notion of regular sets of strings to those of trees and of forests in a unified mathematical approach, and investigate their properties. Then by taking certain one-dimensional expressions of these objects, we come to an interesting subclass of CF languages defined over paired alphabets. They are shown to form a Boolean algebra with the Dyck set as the universe, and to play an important role in the whole class of CF languages. In particular, using the subclass we prove a refinement of the well-known Chomsky---Sch{\"u}tzenberger Theorem, and also prove that the decision procedure for parenthesis grammars can be extended to a broader class of CF grammars.},
    Author = {Takahashi, Masako},
    File = {Generalizations of regular sets and their application to a study of context-free languages - 1-s2.0-S0019995875900583-main.pdf},
    ISSN = {0019-9958},
    Journal = {Information and Control},
    Number = {1},
    Pages = {1-36},
    Title = {Generalizations of regular sets and their application to a study of context-free languages},
    URL = {https://www.sciencedirect.com/science/article/pii/S0019995875900583},
    Volume = {27},
    Year = {1975},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0019995875900583},
    bdsk-url-2 = {https://doi.org/10.1016/S0019-9958(75)90058-3},
    date-added = {2022-06-15 11:32:05 +0200},
    date-modified = {2022-06-15 11:32:05 +0200},
    doi = {10.1016/S0019-9958(75)90058-3}
}

@article{TAKAHASHI19751, Abstract = {We extend the notion of regular sets of strings to those of trees and of forests in a unified mathematical approach, and investigate their properties. Then by taking certain one-dimensional expressions of these objects, we come to an interesting subclass of CF languages defined over paired alphabets. They are shown to form a Boolean algebra with the Dyck set as the universe, and to play an important role in the whole class of CF languages. In particular, using the subclass we prove a refinement of the well-known Chomsky---Sch{\"u}tzenberger Theorem, and also prove that the decision procedure for parenthesis grammars can be extended to a broader class of CF grammars.}, Author = {Takahashi, Masako}, File = {Generalizations of regular sets and their application to a study of context-free languages - 1-s2.0-S0019995875900583-main.pdf}, ISSN = {0019-9958}, Journal = {Information and Control}, Number = {1}, Pages = {1-36}, Title = {Generalizations of regular sets and their application to a study of context-free languages}, URL = {https://www.sciencedirect.com/science/article/pii/S0019995875900583}, Volume = {27}, Year = {1975}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0019995875900583}, bdsk-url-2 = {https://doi.org/10.1016/S0019-9958(75)90058-3}, date-added = {2022-06-15 11:32:05 +0200}, date-modified = {2022-06-15 11:32:05 +0200}, doi = {10.1016/S0019-9958(75)90058-3} }