Qualitative Action Systems

An extension to action systems is presented facilitating the modeling of continuous behavior in the discrete domain. The original action system formalism has been developed by Back et al. in order to describe parallel and distributed computations of discrete systems, i.e. systems with discrete state space and discrete control. In order to cope with hybrid systems, i.e. systems with continuous evolution and discrete control, two extensions have been proposed: hybrid action systems and continuous action systems. Both use differential equations (relations) to describe continuous evolution. Our version of action systems takes an alternative approach by adding a level of abstraction: continuous behavior is modeled by Qualitative Differential Equations that are the preferred choice when it comes to specifying abstract and possibly non-deterministic requirements of continuous behavior. Because their solutions are transition systems, all evolutions in our qualitative action systems are discrete. Based on hybrid action systems, we develop a new theory of qualitative action systems and discuss how we have applied such models in the context of automated test-case generation for hybrid systems.