Graph Homomorphisms and Qualitative Software System Analysis

In this paper we present a mathematical model based on graph homomorphisms permitting the analysis and the behavioral envisioning of software based systems. We first try to explain why a qualitative approach is needed and which are the limitations and problems of quantitative analysis techniques. Follow some results of a qualitative abstraction tool and some simple application examples on telecommunication protocol software. We then introduce the concept of a system qualitative graph and the role of graph homomorphisms for modeling a software as a continuous phase transition map operating on an abstract data space. In our presentation this model has been successfully applied to software based systems but it can be generalized to any hybrid system. We finish with the presentation of the underlying mathematical framework and some properties of graph homomorphism invariants. Key-Words: software engineering, qualitative reasoning, software testing, dynamic system analysis, graph homomorphisms, software phase spaces.