Crossing the Bridge between Similar Games

Specifications and implementations of complex physical systems tend to differ as low level effects such as sampling are often ignored when high level models are created. Thus, the low level models are often not exact refinements of the high level specification. However, they are similar to those. To bridge the gap between those models, we study robust simulation relations for hybrid systems. We identify a family of robust simulation relations that allow for certain bounded deviations in the behavior of a system specification and its implementation in both values of the system variables and timings. We show that for this relaxed version of simulation a broad class of logical properties is preserved. The question whether two systems are in simulation relation can be reduced to a reach avoid problem for hybrid games. We provide a sufficient condition under which a winning strategy for these games exists.