@article{KirstenQuaas:IPL:2011,
    Abstract = {A recognizable series over the semiring of the integers is a function that maps each word over an alphabet to an integer. The support of such a series consists of all those words which are not mapped to zero. It is long known that there are recognizable series whose support is not a recognizable, but a context-free language. However, the problem of deciding whether the support of a given recognizable series is recognizable was never considered. Here we show that this problem is undecidable. The proof relies on an encoding of an instance of Postʼs correspondence problem.},
    Author = {Kirsten, D. and Quaas, K.},
    File = {Recognizablity of the support of recognizable series over the semiring of integers is undecidable - 1-s2.0-S0020019011000548-main.pdf},
    ISSN = {0020-0190},
    Journal = {Information Processing Letters},
    Keywords = {Formal languages, Formal power series, Weighted automata, Postʼs correspondence problem, Supports},
    Number = {10},
    Pages = {500--502},
    Title = {Recognizability of the support of recognizable series over the semiring of the integers is undecidable},
    URL = {https://www.sciencedirect.com/science/article/pii/S0020019011000548},
    Volume = {111},
    Year = {2011},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0020019011000548},
    bdsk-url-2 = {https://doi.org/10.1016/j.ipl.2011.02.014},
    date-added = {2023-08-15 10:49:04 +0200},
    date-modified = {2023-08-15 16:22:00 +0200},
    doi = {10.1016/j.ipl.2011.02.014}
}

@article{KirstenQuaas:IPL:2011, Abstract = {A recognizable series over the semiring of the integers is a function that maps each word over an alphabet to an integer. The support of such a series consists of all those words which are not mapped to zero. It is long known that there are recognizable series whose support is not a recognizable, but a context-free language. However, the problem of deciding whether the support of a given recognizable series is recognizable was never considered. Here we show that this problem is undecidable. The proof relies on an encoding of an instance of Postʼs correspondence problem.}, Author = {Kirsten, D. and Quaas, K.}, File = {Recognizablity of the support of recognizable series over the semiring of integers is undecidable - 1-s2.0-S0020019011000548-main.pdf}, ISSN = {0020-0190}, Journal = {Information Processing Letters}, Keywords = {Formal languages, Formal power series, Weighted automata, Postʼs correspondence problem, Supports}, Number = {10}, Pages = {500--502}, Title = {Recognizability of the support of recognizable series over the semiring of the integers is undecidable}, URL = {https://www.sciencedirect.com/science/article/pii/S0020019011000548}, Volume = {111}, Year = {2011}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0020019011000548}, bdsk-url-2 = {https://doi.org/10.1016/j.ipl.2011.02.014}, date-added = {2023-08-15 10:49:04 +0200}, date-modified = {2023-08-15 16:22:00 +0200}, doi = {10.1016/j.ipl.2011.02.014} }