Quantitative program dependence graphs

Abstract

This paper develops a novel approach that analyses dependencies of programs in a quantitative aspect. We introduce a definition of Quantitative Program Dependence Graph (QPDG) which can be used to model a program's behaviour given spaces of inputs. The programs we consider are in a core while-language. We present the semantics for the purpose of building QPDGs. The QPDG reasons about the program's quantitative uncertainty behaviours based on a probabilistic analysis. It can be used to characterise dependence analysis of programs in a quantitative way. We also provides an optimisation of the QPDG by doing slicing in order to perform a flow analysis, e.g., how input variables at the source node might affect a given output variable at the target node and how much. © 2012 Springer-Verlag.