@article{Korovina:2008aa,
    Abstract = {We study finite bisimulations of dynamical systems in ℝndefined by Pfaffian maps. The pure existence of finite bisimulations for a more general class of o-minimal systems was shown in Brihaye et al. (Lecture Notes in Comput. Sci. 2993, 219--233, 2004), Davoren (Theor. Inf. Appl. 33(4/5), 357--382, 1999), Lafferriere et al. (Math. Control Signals Syst. 13, 1--21, 2000). In Lecture Notes in Comput. Sci. 3210, 2004, the authors proved a double exponential upper bound on the size of a bisimulation in terms of the size of description of the dynamical system. In the present paper we improve it to a single exponential upper bound, and show that this bound is tight, by exhibiting a parameterized class of systems on which it is attained.},
    Author = {Korovina, Margarita and Vorobjov, Nicolai},
    Date = {2008/12/01},
    File = {Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems - korovina2007 - b.pdf},
    ISBN = {1433-0490},
    Journal = {Theory of Computing Systems},
    Number = {3},
    Pages = {498--515},
    Title = {Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems},
    URL = {https://doi.org/10.1007/s00224-007-9019-4},
    Volume = {43},
    Year = {2008},
    bdsk-url-1 = {https://doi.org/10.1007/s00224-007-9019-4},
    date-added = {2023-02-05 07:41:41 +0100},
    date-modified = {2023-02-05 07:41:41 +0100},
    id = {Korovina2008},
    doi = {10.1007/s00224-007-9019-4}
}

@article{Korovina:2008aa, Abstract = {We study finite bisimulations of dynamical systems in ℝndefined by Pfaffian maps. The pure existence of finite bisimulations for a more general class of o-minimal systems was shown in Brihaye et al. (Lecture Notes in Comput. Sci. 2993, 219--233, 2004), Davoren (Theor. Inf. Appl. 33(4/5), 357--382, 1999), Lafferriere et al. (Math. Control Signals Syst. 13, 1--21, 2000). In Lecture Notes in Comput. Sci. 3210, 2004, the authors proved a double exponential upper bound on the size of a bisimulation in terms of the size of description of the dynamical system. In the present paper we improve it to a single exponential upper bound, and show that this bound is tight, by exhibiting a parameterized class of systems on which it is attained.}, Author = {Korovina, Margarita and Vorobjov, Nicolai}, Date = {2008/12/01}, File = {Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems - korovina2007 - b.pdf}, ISBN = {1433-0490}, Journal = {Theory of Computing Systems}, Number = {3}, Pages = {498--515}, Title = {Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems}, URL = {https://doi.org/10.1007/s00224-007-9019-4}, Volume = {43}, Year = {2008}, bdsk-url-1 = {https://doi.org/10.1007/s00224-007-9019-4}, date-added = {2023-02-05 07:41:41 +0100}, date-modified = {2023-02-05 07:41:41 +0100}, id = {Korovina2008}, doi = {10.1007/s00224-007-9019-4} }