@article{KOROVINA201032,
    Abstract = {Suppose that the state space of a dynamical system has a finite partition, and each element of the partition is labelled by a letter of some alphabet. Then every trajectory of the system is naturally labelled by a word in this alphabet. This word is called the combinatorial type of the trajectory. In applications it is important to decide whether among a certain family of trajectories there is at least one trajectory of a given type, or whether all the trajectories in this family have the same type. In this paper we construct algorithms for solving this sort of questions for a wide class of Pfaffian dynamical systems, which have elementary (doubly-exponential) upper complexity bounds.},
    Author = {Korovina, Margarita and Vorobjov, Nicolai},
    File = {Computing combinatorial types of trajectories in Pfaffian Dynamics - 1-s2.0-S1567832609000095-main - b.pdf},
    ISSN = {1567-8326},
    Journal = {The Journal of Logic and Algebraic Programming},
    Keywords = {Dynamical systems, o-Minimality, Pfaffian functions},
    Note = {Speical Issue: Logic, Computability and Topology in Computer Science: A New Perspective for Old Disciplines},
    Number = {1},
    Pages = {32-37},
    Title = {Computing combinatorial types of trajectories in Pfaffian Dynamics},
    URL = {https://www.sciencedirect.com/science/article/pii/S1567832609000095},
    Volume = {79},
    Year = {2010},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S1567832609000095},
    bdsk-url-2 = {https://doi.org/10.1016/j.jlap.2009.02.004},
    date-added = {2023-02-04 08:47:57 +0100},
    date-modified = {2023-02-04 08:47:57 +0100},
    doi = {10.1016/j.jlap.2009.02.004}
}

@article{KOROVINA201032, Abstract = {Suppose that the state space of a dynamical system has a finite partition, and each element of the partition is labelled by a letter of some alphabet. Then every trajectory of the system is naturally labelled by a word in this alphabet. This word is called the combinatorial type of the trajectory. In applications it is important to decide whether among a certain family of trajectories there is at least one trajectory of a given type, or whether all the trajectories in this family have the same type. In this paper we construct algorithms for solving this sort of questions for a wide class of Pfaffian dynamical systems, which have elementary (doubly-exponential) upper complexity bounds.}, Author = {Korovina, Margarita and Vorobjov, Nicolai}, File = {Computing combinatorial types of trajectories in Pfaffian Dynamics - 1-s2.0-S1567832609000095-main - b.pdf}, ISSN = {1567-8326}, Journal = {The Journal of Logic and Algebraic Programming}, Keywords = {Dynamical systems, o-Minimality, Pfaffian functions}, Note = {Speical Issue: Logic, Computability and Topology in Computer Science: A New Perspective for Old Disciplines}, Number = {1}, Pages = {32-37}, Title = {Computing combinatorial types of trajectories in Pfaffian Dynamics}, URL = {https://www.sciencedirect.com/science/article/pii/S1567832609000095}, Volume = {79}, Year = {2010}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S1567832609000095}, bdsk-url-2 = {https://doi.org/10.1016/j.jlap.2009.02.004}, date-added = {2023-02-04 08:47:57 +0100}, date-modified = {2023-02-04 08:47:57 +0100}, doi = {10.1016/j.jlap.2009.02.004} }