Theory of Computing Systems

, Volume 41, Issue 1, pp 33–48 | Cite as

Optimal Semicomputable Approximations to Reachable and Invariant Sets

  • Pieter CollinsEmail author
Open Access


In this paper we consider the computation of reachable, viable and invariant sets for discrete-time systems. We use the framework of type-two effectivity, in which computations are performed by Turing machines with infinite input and output tapes, with the representations of computable topology. We see that the reachable set is lower-semicomputable, and the viability and invariance kernels are upper-semicomputable. We then define an upper-semicomputable over-approximation to the reachable set, and lower-semicomputable under-approximations to the viability and invariance kernels, and show that these approximations are optimal.


Multivalued Function Computable Function Compact Hausdorff Space Viability Kernel Vietoris Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Centrum voor Wiskunde en Informatica, Postbus 940791090 GB AmsterdamThe Netherlands

Personalised recommendations