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.

Original language | English |
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Title of host publication | Computer Science Logic, Proceedings |
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Pages | 430-441 |
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Number of pages | 12 |
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Volume | 3210 |
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Publication status | Published - 2004 |
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Name | Lecture Notes in Computer Science |
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ID number: ISI:000224024900033