On Algorithmic and Heuristic Approaches to Integral Problems in the Polyhedron Model with Non-linear Parameters

The polyhedron model provides one possible approach to model-based program analysis and transformation. Over the years, it has undergone many improvements in order to handle a still growing class of programs. A recent approach enabled the use of non-linear parameters, which was in that generality not possible before. While this new framework uses real quantifier elimination, the present work examines possibilities to describe the integral solutions to certain problems occurring in the polyhedron model exactly. In particular, we study the solvability of systems of linear Diophantine equations in one and several non-linear integral parameters and demonstrate the applicability of the developed methods for Banerjee’s data dependence analysis.