Order:
  1.  5
    Cell Decomposition and Dimension Function in the Theory of Closed Ordered Differential Fields.Thomas Brihaye, Christian Michaux & Cédric Rivière - 2009 - Annals of Pure and Applied Logic 159 (1-2):111-128.
    In this paper we develop a differential analogue of o-minimal cell decomposition for the theory CODF of closed ordered differential fields. Thanks to this differential cell decomposition we define a well-behaving dimension function on the class of definable sets in CODF. We conclude this paper by proving that this dimension is closely related to both the usual differential transcendence degree and the topological dimension associated, in this case, with a natural differential topology on ordered differential fields.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  2.  38
    A Note on the Undecidability of the Reachability Problem for o‐Minimal Dynamical Systems.Thomas Brihaye - 2006 - Mathematical Logic Quarterly 52 (2):165-170.
    In this paper we prove that the reachability problem is BSS-undecidable for o-minimal dynamical systems.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  3.  21
    Weighted o-Minimal Hybrid Systems.Patricia Bouyer, Thomas Brihaye & Fabrice Chevalier - 2009 - Annals of Pure and Applied Logic 161 (3):268-288.
    We consider weighted o-minimal hybrid systems, which extend classical o-minimal hybrid systems with cost functions. These cost functions are “observer variables” which increase while the system evolves but do not constrain the behaviour of the system. In this paper, we prove two main results: optimal o-minimal hybrid games are decidable; the model-checking of WCTL, an extension of CTL which can constrain the cost variables, is decidable over that model. This has to be compared with the same problems in the framework (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark