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Abstract Program Slicing: an Abstract Interpretation-based approach to Program Slicing

In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and reference values, and relies on the notion of abstract dependencies between program components (statements). The different forms of (backward) abstract slicing are added to an existing formal framework where traditional, non-abstract forms of slicing could be compared. The extended framework allows us to appreciate that abstract slicing is a generalization of traditional slicing, since traditional slicing (dealing with syntactic dependencies) is generalized by (semantic) non-abstract forms of slicing, which are actually equivalent to an abstract form where the identity abstraction is performed on data. Sound algorithms for computing abstract dependencies and a systematic characterization of program slices are provided, which rely on the notion of agreement between program states.