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 (...) of timed automata where both problems are undecidable in general, while they are decidable for the restricted class of one-clock timed automata. (shrink)

We extend some of the classical connections between automata and logic due to Büchi [5] and McNaughton and Papert [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called ’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich [15]. We also identify a “counter-free” subclass of ’s which characterise the first-order definable languages (...) of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic Chevalier et al. [6] and [7]. (shrink)