Widening the Boundary Between Decidable and Undecidable Hybrid Systems

Abstract. We revisited decidability of the reachability problem for low dimensional hybridsystems. Eventhoughmanyattemptshavebeendone todraw theboundarybetween decidable and undecidable hybridsystems there are still many open problems in between. In this paper we show that the reachability question for some two dimensional hybrid systems are undecidable and that for other 2-dim systems this question remains unanswered, showing that it is as hard as the reachability problem for Piecewise Affine Maps, that is a well known open problem. 1