## Parametric and Termination-Sensitive Control Dependence

### Feng Chen (University of Illinois at Urbana Champaign) and Grigore Rosu (University of Illinois at Urbana Champaign)

## Abstract

A parametric approach to control dependence is presented, where the parameter is any prefix-invariant property on paths in the control-flow graph. Existing control dependencies, both direct and indirect, can be obtained as instances of the parametric framework for particular properties on paths. A novel control dependence relation, called termination-sensitive control dependence, is obtained also as an instance of the parametric framework. This control dependence is sensitive to the termination information of loops, which can be given as annotations on loops. If all loops are annotated as terminating then it becomes the classic control dependence, while if all loops are annotated as non-terminating then it becomes the weak control dependence; since in practice some loops are terminating and others are not, termination-sensitive control dependence is expected to improve the precision of analysis tools using it. The unifying formal framework for direct and indirect control dependencies suggests also, in a natural way, a unifying terminology for the various notions of control dependency, which is also proposed in this paper. Finally, a worst-case O(n^2) algorithm to compute the indirect termination-sensitive control dependence for languages like Java and C# is given, avoiding the O(n^3) complexity of the trivial algorithm calculating the transitive closure of the direct dependence.