Refining abstract interpretations

interpretation techniques prove properties of programs by computing abstract fixpoints. All such analyses suffer from the possibility of false errors. We present a dag-based abstraction refinement technique to automatically refine such abstract interpretations and reduce false errors. This technique refines precision loss due to widen operator by a new interpolated widen operator and refines precision loss due to join operator by disjunctions. We prove the soundness and progress properties of this abstraction refinement procedure.