@inproceedings{10.1007/978-3-540-30124-0_33,
    Abstract = {It is well known that in an o-minimal hybrid system the continuous and discrete components can be separated, and therefore the problem of finite bisimulation reduces to the same problem for a transition system associated with a continuous dynamical system. It was recently proved by several authors that under certain natural assumptions such finite bisimulation exists. In the paper we consider o-minimal systems defined by Pfaffian functions, either implicitly (via triangular systems of ordinary differential equations) or explicitly (by means of semi-Pfaffian maps). We give explicit upper bounds on the sizes of bisimulations as functions of formats of initial dynamical systems. We also suggest an algorithm with an elementary (doubly-exponential) upper complexity bound for computing finite bisimulations of these systems.},
    Address = {Berlin, Heidelberg},
    Author = {Korovina, Margarita and Vorobjov, Nicolai},
    BookTitle = {Computer Science Logic},
    Editor = {Marcinkowski, Jerzy and Tarlecki, Andrzej},
    File = {Pfaffian hybrid systems - KV04lncs - a - a - a - w.pdf},
    ISBN = {978-3-540-30124-0},
    Pages = {430--441},
    Publisher = {Springer Berlin Heidelberg},
    Title = {Pfaffian Hybrid Systems},
    Year = {2004},
    date-added = {2020-03-01 17:59:38 +0100},
    date-modified = {2020-03-01 17:59:38 +0100},
    doi = {10.1007/978-3-540-30124-0_33}
}

@inproceedings{10.1007/978-3-540-30124-0_33, Abstract = {It is well known that in an o-minimal hybrid system the continuous and discrete components can be separated, and therefore the problem of finite bisimulation reduces to the same problem for a transition system associated with a continuous dynamical system. It was recently proved by several authors that under certain natural assumptions such finite bisimulation exists. In the paper we consider o-minimal systems defined by Pfaffian functions, either implicitly (via triangular systems of ordinary differential equations) or explicitly (by means of semi-Pfaffian maps). We give explicit upper bounds on the sizes of bisimulations as functions of formats of initial dynamical systems. We also suggest an algorithm with an elementary (doubly-exponential) upper complexity bound for computing finite bisimulations of these systems.}, Address = {Berlin, Heidelberg}, Author = {Korovina, Margarita and Vorobjov, Nicolai}, BookTitle = {Computer Science Logic}, Editor = {Marcinkowski, Jerzy and Tarlecki, Andrzej}, File = {Pfaffian hybrid systems - KV04lncs - a - a - a - w.pdf}, ISBN = {978-3-540-30124-0}, Pages = {430--441}, Publisher = {Springer Berlin Heidelberg}, Title = {Pfaffian Hybrid Systems}, Year = {2004}, date-added = {2020-03-01 17:59:38 +0100}, date-modified = {2020-03-01 17:59:38 +0100}, doi = {10.1007/978-3-540-30124-0_33} }