Treffer: Computational Homology for Software Validation

The research objective, to develop new objective tools to aid in software verification and validation based on topological methods, found that the application of topology to software with compound non-numerical, non-metric data-types, proved to be too course-grained to provide a mathematical foundation for rigorously reasoning about the evolution of the compound state of executing software and overcame this difficult by applying a refinement of topological structure, called convergence structure (CS). CS was applied to serve as the mathematical underpinning for specifying the evolution of compound states by providing an analytical foundation for such state evolution. Such a foundation is geometric in character and is derivable from symmetries in the state space by group-theoretic means and then determining CS with respect to which the symmetries are continuous. Student D. Patten investigated CS methods on discrete structures for the purpose of rigorously formulating hybrid dynamical systems involving discrete structure data-types to aid in developing formal specifications for object-oriented & similar software involving compound data-types. ; The original document contains color images.