Qualitative Software Dynamics

In this paper we present a qualitative graph-based formalism for the analysis and the envisioning of software based system dynamics. We first present the main difficulties of dynamic software analysis. Follow some results of a qualitative abstraction tool and some application examples. We then introduce the concept of a system qualitative graph, and the role of graph homomorphisms. Software is considered as a general system endowed with a continuous phase transition map operating on an abstract data space that is a graph. Our approach formalizes the most widespread dynamic testing techniques. We finish with the presentation of the underlying mathematical qualitative framework and some basic properties of graph homomorphism invariants