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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… (More)

In this paper we study Pfaffian hybrid systems which were first introduced in [9]. Pfaffian hybrid systems are a sub-class of o-minimal hybrid systems which capture rich continuous dynamics and yet can be studied using finite bisimulations. The existence of finite bisimulations for o-minimal hybrid systems has been shown by several authors (see e.g. [2, 3,… (More)

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a… (More)

Characteristic properties of majorant-computable real-valued functions are studied. A formal theory of computability over the reals which satisses the requirements of numerical analysis used in Computer Science is constructed on the base of the deenition of majorant-computa-bility proposed in 13]. A model-theoretical characterization of… (More)

In this paper we present a study of definability properties of fixed points of effective operators on abstract structures without the equality test. In particular we prove that Gandy theorem holds for the reals without the equality test. This provides a useful tool for dealing with recursive definitions using Σ-formulas.