On Temporal Path Conditions in Dependence Graphs

Program dependence graphs are a well-established device to represent possible information flow in a program. Path conditions in dependence graphs have been proposed to express more detailed circumstances of a particular flow; they provide precise necessary conditions for information flow along a path or chop in a dependence graph. Ordinary Boolean path conditions however cannot express temporal properties, e.g. that for a specific flow it is necessary that some condition holds, and later another specific condition holds. In this contribution, we introduce temporal path conditions, which extend ordinary path conditions by temporal operators in order to express temporal dependencies between conditions for a flow. We present motivating examples, generation and simplification rules, application of model checking to generate witnesses for a specific flow, and a case study. We prove the following soundness property: if a temporal path condition for a path is satisfiable, then the ordinary boolean path condition for the path is satisfiable. The converse does not hold, indicating that temporal path conditions are more precise.