Interprocedural Polynomial Invariants Acknowledgement I Would like to Thank

This thesis describes techniques for static analysis of polynomial equalities in interprocedural programs. It elaborates on approaches for analysing polynomial equalities over different domains as well as techniques to apply polynomial analysis to infer interprocedurally valid equalities of uninterpreted terms. This work is organised in three major theoretical parts, followed by a practical part. In the first part forward and backward frameworks for inferring polynomial equalities are presented and extended to deal with procedure calls. It is shown how both approaches make use of polynomial ideals as abstraction of program states. Since the performance of operations on polynomial ideals is highly dependent on the way the ideals are represented in detail, the most crucial representation issues are highlighted here. In the second part, values of variables are treated as integers modulo a power of two which coincides with the treatment of integers in most current architectures. This part provides methods for inferring polynomial invariants modulo 2. The third part is dedicated to equalities of uninterpreted terms, so called Herbrand equalities. It is inspected in how far polynomial ideals can be applied to interprocedurally infer Herbrand equalities. This gives rise to a novel subclass of the general problem which can be analysed precisely. In the practical part, I finally elaborate on my implementation of a framework for performing interprocedural program analyses on real-world code. I give an overview over the architecture of the analyser’s fixpoint iteration engine, target architecture plugin system and a short description how to implement other analyses in this framework.